9th Class Mathematics Heron's Formula Question Bank

done Heron's Formula Total Questions - 50

• question_answer1)
  The perimeter of a triangular field is 144 m and the ratio of its sides is 3 :4 :5. Find the area of the field.
  A)
   864 sq. m         done clear
  B)
   764 sq. m         done clear
  C)
   854 sq. m         done clear
  D)
   754 sq. m         done clear
  View Solution play_arrow

• question_answer2)
  One side of an equilateral triangle is 8 cm. What is its area?
  A)
  \[12\sqrt{3}\,c{{m}^{2}}\]        done clear
  B)
    \[16\sqrt{3}\,c{{m}^{2}}\]        done clear
  C)
  \[8\sqrt{3}\,c{{m}^{2}}\]         done clear
  D)
    \[48\sqrt{3}\,c{{m}^{2}}\]                    done clear
  View Solution play_arrow

• question_answer3)
  The base of an isosceles triangle is 12 cm and its perimeter is 32 cm. What is its area?
  A)
   12sq.cm                       done clear
  B)
   36 sq.cm          done clear
  C)
     24 sq.cm      done clear
  D)
                 48 sq.cm                      done clear
  View Solution play_arrow

• question_answer4)
  The edges of a triangular board are 6 cm, 8 cm and 10 cm. What is the cost of painting it at the rate of 9 paise per\[~c{{m}^{2}}\]?
  A)
  Rs. 2.00             done clear
  B)
  Rs. 2.16 done clear
  C)
    Rs. 2.48          done clear
  D)
    Rs. 3.00 done clear
  View Solution play_arrow

• question_answer5)
  What is the area of a triangle whose sides are 13 cm, 14 cm and 15 cm?
  A)
   84 sq.cm          done clear
  B)
   64 sq.cm          done clear
  C)
     82 sq.cm      done clear
  D)
     48 sq.cm          done clear
  View Solution play_arrow

• question_answer6)
  Two adjacent sides of a parallelogram are 5 cm and 3.5 cm. One of its diagonals is 6.5 cm. Find the area of parallelogram.
  A)
  \[5\sqrt{3}\,c{{m}^{2}}\]                     done clear
  B)
  \[10\sqrt{3}\,c{{m}^{2}}\] done clear
  C)
  \[15\sqrt{3}\,c{{m}^{2}}\]        done clear
  D)
    \[20\sqrt{3}\,c{{m}^{2}}\]        done clear
  View Solution play_arrow

• question_answer7)
  The sides of a triangle are in the ratio of 13:14:15 and its perimeter is 84 cm. Determine the area of the triangle.
  A)
  \[~136\,c{{m}^{2}}\]                          done clear
  B)
  \[~236\,c{{m}^{2}}\]  done clear
  C)
  \[~336\text{ }c{{m}^{2}}\]      done clear
  D)
    \[~436\text{ }c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer8)
  What is the area of a parallelogram whose diagonal is 6.8 cm and the perpendicular distance of this diagonal from an opposite vertex is 7.5 cm?
  A)
  \[25.5\,c{{m}^{2}}\]    done clear
  B)
    \[11.9\,c{{m}^{2}}\]    done clear
  C)
  \[12.5\,c{{m}^{2}}\]    done clear
  D)
    \[51\,c{{m}^{2}}\]                   done clear
  View Solution play_arrow

• question_answer9)
  The adjacent sides of a parallelogram are 4 cm and 9 cm. What is the ratio of its altitudes?
  A)
   16 : 81                         done clear
  B)
   9 : 4                 done clear
  C)
   2 : 3                   done clear
  D)
   3 : 2 done clear
  View Solution play_arrow

• question_answer10)
  The perimeter of a rhombus is 52 cm and one of its diagonals is 24 cm. Determine the length of the other diagonal.
  A)
   24 cm                          done clear
  B)
   10 cm  done clear
  C)
  \[2\frac{1}{6}cm\]         done clear
  D)
     12cm done clear
  View Solution play_arrow

• question_answer11)
  The area of a rhombus is \[28\text{ }c{{m}^{2}}\]and one of its diagonals is 4 cm. What is its perimeter?
  A)
  \[4\sqrt{53}\,cm\]                       done clear
  B)
  \[36\,cm\]          done clear
  C)
    \[2\sqrt{53}\,cm\]           done clear
  D)
     52 cm              done clear
  View Solution play_arrow

• question_answer12)
  The adjacent sides of a parallelogram are 8 cm and 9 cm. The diagonal joining the ends of these sides is 13 cm. Find its area.
  A)
  \[72\,c{{m}^{2}}\]                   done clear
  B)
  \[12\sqrt{35}\,c{{m}^{2}}\]      done clear
  C)
  \[24\sqrt{35}\,c{{m}^{2}}\]        done clear
  D)
    \[150\,c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer13)
  The sides of a triangle are 11 cm, 15 cm and 16 cm. Find the measure of the altitude to the largest side.
  A)
  \[30\sqrt{7}\,cm\]                       done clear
  B)
   \[\frac{15\sqrt{7}}{2}\,cm\]       done clear
  C)
   \[\frac{15\sqrt{7}}{4}\,cm\]       done clear
  D)
     30 cm done clear
  View Solution play_arrow

• question_answer14)
  The perimeter of a triangle is 60 m and its sides are in the ratio 5:12:13, Find the length of the altitude of the triangle corresponding to the longest side.
  A)
   \[9\frac{3}{13}m\]                    done clear
  B)
  \[5\frac{4}{12}m\]         done clear
  C)
  \[6\frac{9}{11}m\]         done clear
  D)
    \[7\frac{2}{15}m\] done clear
  View Solution play_arrow

• question_answer15)
  If the altitude of an equilateral triangle is \[\sqrt{6}\,cm,\]what is its area?
  A)
  \[2\sqrt{3}\,c{{m}^{2}}\]                                 done clear
  B)
  \[2\sqrt{2}\,c{{m}^{2}}\]         done clear
  C)
    \[3\sqrt{3}\,c{{m}^{2}}\]         done clear
  D)
    \[6\sqrt{2}\,c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer16)
  The sides of an equilateral triangle are (2a - b + 5), (a + b) and (2b - a + 2). What is the area of the triangle?
  A)
  \[\frac{\sqrt{3}}{4}\times {{a}^{2}}\]               done clear
  B)
  \[\frac{\sqrt{3}}{4}\times {{b}^{2}}\]   done clear
  C)
    \[\frac{\sqrt{3}}{4}\times 49\]     done clear
  D)
    \[\frac{\sqrt{3}}{4}\times 81\]     done clear
  View Solution play_arrow

• question_answer17)
  In \[\Delta ABC,AB=6cm,\,BC=7cm\]and AC= 5 cm. What is the area of \[\Delta ABC?\]
  A)
  \[6\sqrt{6}\,c{{m}^{2}}\]                     done clear
  B)
  \[6\sqrt{3}\,c{{m}^{2}}\]         done clear
  C)
  \[6\sqrt{2}\,c{{m}^{2}}\]         done clear
  D)
    \[9\sqrt{6}\,c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer18)
  If the angles of a triangle are in the ratio 5:3:7, what is such a triangle called?
  A)
   An acute angled triangle done clear
  B)
   An obtuse angled triangle done clear
  C)
   A right triangle done clear
  D)
   An isosceles triangle done clear
  View Solution play_arrow

• question_answer19)
  The base of an isosceles right triangle is 30 cm. Find its area.
  A)
   \[225\,c{{m}^{2}}\]                done clear
  B)
  \[225\sqrt{3}\,c{{m}^{2}}\]      done clear
  C)
  \[225\sqrt{2}\,c{{m}^{2}}\]   done clear
  D)
    \[450\,c{{m}^{2}}\]                 done clear
  View Solution play_arrow

• question_answer20)
  Which of the following is the area of an isosceles triangle with equal sides b and base a?
  A)
  \[\frac{a}{2}\sqrt{{{b}^{2}}-{{a}^{2}}}\]      done clear
  B)
    \[\frac{1}{2}a\sqrt{4{{b}^{2}}-{{a}^{2}}}\] done clear
  C)
    \[\frac{a}{4}\sqrt{{{b}^{2}}-{{a}^{2}}}\]      done clear
  D)
    \[\frac{a}{4}\sqrt{4{{b}^{2}}-{{a}^{2}}}\]   done clear
  View Solution play_arrow

• question_answer21)
  An isosceles right triangle has area \[8\text{ }c{{m}^{2}}.\] What is the length of its hypotenuse?
  A)
  \[\sqrt{32}\,cm\]             done clear
  B)
  \[\sqrt{16}\,cm\] done clear
  C)
  \[\sqrt{48}\,cm\] done clear
  D)
    \[\sqrt{24}\,cm\]   done clear
  View Solution play_arrow

• question_answer22)
  A farmer divided his field which is in the shape of a rhombus of side 100 m between his two sons equally. If the line of division is 160 m, what area of the field did each son get?
  A)
   4840 sqm         done clear
  B)
  \[~1400\,{{m}^{2}}\]  done clear
  C)
  \[4800\,{{m}^{2}}\]    done clear
  D)
    \[~3600\text{ }{{m}^{2}}\]     done clear
  View Solution play_arrow

• question_answer23)
  The sides of a triangle are 50 cm, 78 cm and 112 cm. Find the smallest altitude.
  A)
   20 cm              done clear
  B)
   30 cm  done clear
  C)
   40 cm        done clear
  D)
     50 cm done clear
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• question_answer24)
  Suman made an arrangement with shaded and unshaded paper sheets as shown in the figure. Find the total area of the shaded paper sheets used in making the arrangement.
  A)
  \[\frac{9}{4}\sqrt{55}\,c{{m}^{2}}\]                 done clear
  B)
  \[\frac{8}{5}\sqrt{11}\,c{{m}^{2}}\]     done clear
  C)
    \[\frac{16}{9}\sqrt{55}\,c{{m}^{2}}\]   done clear
  D)
    \[\frac{6}{5}\sqrt{11}\,c{{m}^{2}}\]     done clear
  View Solution play_arrow

• question_answer25)
  The base and hypotenuse of a right triangle are respectively 5 cm and 13 cm long. Find its area.
  A)
  \[25\,c{{m}^{2}}\]                   done clear
  B)
  \[28\,c{{m}^{2}}\]       done clear
  C)
  \[30\,c{{m}^{2}}\]       done clear
  D)
    \[40\,c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer26)
  White and grey coloured triangular plastic sheets are used to make a toy as shown in figure. Find the difference in areas of shaded and unshaded coloured sheets used for making the toy.
  A)
  \[1\,c{{m}^{2}}\]                     done clear
  B)
  \[0\,c{{m}^{2}}\]         done clear
  C)
  \[5\sqrt{2}\,c{{m}^{2}}\]         done clear
  D)
    \[16\sqrt{2}\,c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer27)
  What is the area of an isosceles triangle having base 2 cm and the length of one of the equal sides 4 cm?
  A)
  \[\sqrt{15}c{{m}^{2}}\]                       done clear
  B)
  \[\sqrt{\frac{15}{2}}c{{m}^{2}}\]        done clear
  C)
  \[2\sqrt{15}c{{m}^{2}}\]          done clear
  D)
    \[4\sqrt{15}c{{m}^{2}}\]  done clear
  View Solution play_arrow

• question_answer28)
  \[\Delta ABC\]is an equilateral triangle where each side is of length 'a' units. Find its area if its perimeter is 150 m.
  A)
  \[1000\sqrt{3}\,{{m}^{2}}\]                  done clear
  B)
  \[250\sqrt{3}\,{{m}^{2}}\]       done clear
  C)
  \[500\sqrt{3}\,{{m}^{2}}\]       done clear
  D)
    \[625\sqrt{3}\,{{m}^{2}}\]    done clear
  View Solution play_arrow

• question_answer29)
  If the area of an isosceles right triangle is \[8\,c{{m}^{2}},\]what is its perimeter?
  A)
  \[\left( 8+\sqrt{2} \right)cm\]                    done clear
  B)
  \[\left( 8+4\sqrt{2} \right)cm\] done clear
  C)
    \[\left( 4+8\sqrt{2} \right)cm\]  done clear
  D)
    \[100\sqrt{3}\,{{m}^{2}}\]       done clear
  View Solution play_arrow

• question_answer30)
  The perimeter of an equilateral triangle is 60 m. What is its area?
  A)
  \[10\sqrt{3}\,{{m}^{2}}\]                     done clear
  B)
  \[15\sqrt{3}\,{{m}^{2}}\]         done clear
  C)
  \[20\sqrt{3}\,{{m}^{2}}\]         done clear
  D)
    \[100\sqrt{3}\,{{m}^{2}}\]    done clear
  View Solution play_arrow

• question_answer31)
  A square and an equilateral triangle have equal perimeters. If the diagonal of the square is \[12\sqrt{2}\,cm,\]what is the area of the triangle?
  A)
  \[24\sqrt{2}\,c{{m}^{2}}\]                    done clear
  B)
  \[24\sqrt{3}\,c{{m}^{2}}\]        done clear
  C)
  \[48\sqrt{3}\,c{{m}^{2}}\]        done clear
  D)
    \[64\sqrt{3}\,c{{m}^{2}}\]        done clear
  View Solution play_arrow

• question_answer32)
  A rhombus shaped field has green grass for 48 cows to graze. If each side of the rhombus is 50 m and its longer diagonal is 80 m, how much area of the grass field will each cow be able to graze in?
  A)
  \[150\,c{{m}^{2}}\]                 done clear
  B)
  \[120\,c{{m}^{2}}\]     done clear
  C)
  \[50\,c{{m}^{2}}\]       done clear
  D)
    \[100\,c{{m}^{2}}\]    done clear
  View Solution play_arrow

• question_answer33)
  The length of the sides of \[\Delta ABC\]are consecutive integers. If\[\Delta ABC\]has the same perimeter as an equilateral triangle with a side of length 9 cm, what is the length of the shortest side of \[\Delta ABC?\]
  A)
   4 cm                            done clear
  B)
   6 cm    done clear
  C)
   8cm                 done clear
  D)
     10 cm done clear
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• question_answer34)
  An umbrella is made by stitching 12 triangular pieces of cloth of two different colours as shown in figure. Each piece measures 40 cm, 40 cm and 18cm. How much cloth of each colour is required for the umbrealla?
  A)
  \[378\sqrt{3}\,c{{m}^{2}}\]                  done clear
  B)
  \[756\sqrt{3}\,c{{m}^{2}}\]      done clear
  C)
  \[252\sqrt{3}\,c{{m}^{2}}\]      done clear
  D)
    \[567\sqrt{3}\,c{{m}^{2}}\]    done clear
  View Solution play_arrow

• question_answer35)
  If the area of an equilateral triangle is \[16\sqrt{3}\,c{{m}^{2}},\] what is the perimeter of the triangle?
  A)
   48 cm              done clear
  B)
   24 cm  done clear
  C)
   12 cm        done clear
  D)
     306 cm done clear
  View Solution play_arrow

• question_answer36)
  Which of the following should we have in order to find the area of a triangle by Herons formula?
  A)
   All the angles done clear
  B)
   Altitudes done clear
  C)
   Two sides and the including angle done clear
  D)
   All the sides done clear
  View Solution play_arrow

• question_answer37)
  If the length of a median of an equilateral triangle is \[x\,cm,\]find its area.
  A)
   \[{{x}^{2}}c{{m}^{2}}\]                  done clear
  B)
  \[\frac{\sqrt{3}}{2}{{x}^{2}}\,c{{m}^{2}}\]   done clear
  C)
  \[\frac{{{x}^{2}}}{\sqrt{3}}c{{m}^{2}}\]       done clear
  D)
    \[\frac{{{x}^{2}}}{2}c{{m}^{2}}\]  done clear
  View Solution play_arrow

• question_answer38)
  A floral design on a floor is made up of 16 triangular tiles of sides 26 cm, 20 cm and 10 cm. The tiles are polished at the rate of 20 p per \[c{{m}^{2}}.\] Find the cost of polishing the tiles. \[(Take\sqrt{14}=3.74.)\]
  A)
  Rs. 195.64           done clear
  B)
  Rs. 216.52           done clear
  C)
  Rs. 287.23     done clear
  D)
  Rs. 325.13 done clear
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• question_answer39)
  A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 15 cm, 14 cm and 13 cm and the parallelogram stands on the side of 15 cm, find the height of the parallelogram.
  A)
   4.2 cm             done clear
  B)
   5.6 cm done clear
  C)
   8.4 cm        done clear
  D)
   2.1 cm done clear
  View Solution play_arrow

• question_answer40)
  What is the length of each side of an equilateral triangle having an area of \[9\sqrt{3}\,c{{m}^{2}}?\]
  A)
   8cm                             done clear
  B)
   36cm   done clear
  C)
   4 cm                done clear
  D)
     6 cm done clear
  View Solution play_arrow

• question_answer41)
  What is the area of a triangle having two sides as 18 cm and 10 cm and perimeter is 42 cm?
  A)
  \[3\sqrt{11}c{{m}^{2}}\]                      done clear
  B)
  \[7\sqrt{11}c{{m}^{2}}\]          done clear
  C)
  \[33\sqrt{7}c{{m}^{2}}\]          done clear
  D)
    \[21\sqrt{11}c{{m}^{2}}\]    done clear
  View Solution play_arrow

• question_answer42)
  A kite in the shape of a square with a diagonal 40 cm and an isosceles triangle of base 10 cm and side 13 cm each is to be made of three different shades as shown in the figure. Find the ratio of each shade used in making the kite,
  A)
   20:20:3 done clear
  B)
   10:10:3 done clear
  C)
   25:35:3      done clear
  D)
   9:11:1 done clear
  View Solution play_arrow

• question_answer43)
  What is the semiperimeter of a scalene triangle of sides k, 2k and 3k?
  A)
   k                                  done clear
  B)
   2k                    done clear
  C)
     3k                    done clear
  D)
     4k done clear
  View Solution play_arrow

• question_answer44)
  A triangle has perimeter 32 cm, one side is 11 cm and difference of other two sides is 5 cm. Determine its area.
  A)
  \[4\sqrt{30}\,c{{m}^{2}}\]                    done clear
  B)
  \[8\sqrt{30}\,c{{m}^{2}}\]        done clear
  C)
  \[6\sqrt{30}\,c{{m}^{2}}\]        done clear
  D)
    \[5\sqrt{30}\,c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer45)
  A triangular park in a city has dimensions \[10\,m\times 90\,m\times 110m.\]A contract is given to a company for planting grass in the park at the rate of Rs. 4000 per hectare. What is the amount to be paid to the company? (Take \[\sqrt{2}=1.414\]and One hectare\[=\text{ }10000\,{{m}^{2}}.\])
  A)
  Rs. 1968.60         done clear
  B)
  Rs. 1698.60         done clear
  C)
  Rs. 1986.60     done clear
  D)
  Rs. 1696.80 done clear
  View Solution play_arrow

• question_answer46)
  Area of a given triangle \[{{x}_{1}}\] square units. If the sides of this triangle are doubled, the area of the new triangle becomes\[{{x}_{2}}\]square units. Calculate the percentage increase in the area.
  A)
   100%               done clear
  B)
   200%   done clear
  C)
   300 %         done clear
  D)
     400 %              done clear
  View Solution play_arrow

• question_answer47)
  In a quadrilateral ABCD if AB = 5 m, BC = 5m, CD = 6m, AD = 6m and diagonal AC = 6 m, what is its area?
  A)
  \[2(4+3\sqrt{3}){{m}^{2}}\]     done clear
  B)
  \[3(4+3\sqrt{3}){{m}^{2}}\] done clear
  C)
     \[5(4+3\sqrt{3}){{m}^{2}}\] done clear
  D)
    \[7(4+3\sqrt{3}){{m}^{2}}\]   done clear
  View Solution play_arrow

• question_answer48)
  In a quadrilateral ABCD if AB = 9 m, BC = 40 m, CD = 28 m, AD = 15 m and \[\angle ABC={{90}^{o}},\]find its area.
  A)
  \[136\,{{m}^{2}}\]                               done clear
  B)
  \[~163\,{{m}^{2}}\]    done clear
  C)
    \[~360\text{ }{{m}^{2}}\]      done clear
  D)
    \[~306\text{ }{{m}^{2}}\]       done clear
  View Solution play_arrow

• question_answer49)
  A rhombus has perimeter 100 m and one of its diagonals is 40 m. Find the area of the rhombus.
  A)
  \[~600\text{ }{{m}^{2}}\]        done clear
  B)
  \[~500\text{ }{{m}^{2}}\]       done clear
  C)
  \[~400\text{ }{{m}^{2}}\]        done clear
  D)
  \[~300\text{ }{{m}^{2}}\]                   done clear
  View Solution play_arrow

• question_answer50)
  A field is in the shape of a trapezium whose parallel sides are 50 m and 15m. The non-parallel sides are 20 m and 25 m. What is the area of the trapezium?
  A)
  \[\frac{900\,\sqrt{6}}{7}{{m}^{2}}\]                done clear
  B)
  \[\frac{1100\,\sqrt{6}}{7}{{m}^{2}}\]   done clear
  C)
  \[\frac{1300\,\sqrt{6}}{7}{{m}^{2}}\]   done clear
  D)
    \[\frac{1500\,\sqrt{6}}{7}{{m}^{2}}\]    done clear
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