# 5th Class Mental Ability Measurement Length, Weight and Capacity Measurement

Measurement

Category : 5th Class

Measurement

Learning Objectives

• Perimeter
• Area
• Volume

Perimeter

Perimeter is referred as the length of the boundary line, which surrounds the area occupied by a geometrical shape.

Perimeters of different geometrical shapes are explained below.

A. Perimeter of a Triangle

A triangles has three sides. Perimeter of a triangle is the sum of its all the three sides.

Perimeter of the triangle $ABC=AB+BC+CA$

Perimeter of a quadrilateral is the sum of the length of its four sides.

In quadrilateral ABCD, perimeter $=AB+BC+CD+DA$

C. Perimeter of a Rectangle

Perimeter of a rectangle = 2 (Length + Breadth).

D. Perimeter of a square $=\mathbf{4}\times \mathbf{side}$.

Perimeter of the square $ABCD=4\times AB$

E. Perimeter of a Circle

Perimeter of a circle $=2\pi r$

Where $~\pi =\frac{22}{7}~=3.14$ and r = radius of the circle

Area

All the geometrical shapes occupies some space. The occupied space by a geometrical shape is called area of that geometrical shape.

Shaded part in the above figures represent area.

Unit of area is $c{{m}^{2}}$or ${{m}^{2}}$.

Areas of different geometrical shapes are listed belowA. Area of a Triangle

Area of a triangle $=1/2\times ~\,base~\times \,height$.

Where base is the one side of a triangle and height is the length of the line segment drawn $90{}^\circ$ on the base of that triangle.

B. Area of a Rectangle

Area of a rectangle$\text{=length }\!\!~\!\!\text{ }\!\!\times\!\!\text{ }\,\text{breadth}$.

Area of the rectangle $PQRS=PQ\times QR$. Where PQ is the length and QR is the breath.

C. Area of a Square

Area of a square $\text{=sid}{{\text{e}}^{\text{2}}}\text{=side }\!\!~\!\!\text{ }\!\!\times\!\!\text{ }\,\text{side}$

Area of the square $PQRS=PQ~\times \,PQ=P{{Q}^{2}}$.

D. Area of a Circle

Area of the circle = $\pi {{r}^{2}}$

Where $\pi =\frac{22}{7}=3.14$

1. Find the perimeter of the following figure.

(a) 22.45 cm                  (b) 23.50 cm

(c) 20.15 cm                  (d) 15.55 cm

(e) None of these

Solution: Perimeter of the figure $=4\text{ }cm+3\text{ }cm+4\text{ }cm+2.5\text{ }cm+5\text{ }cm+5\text{ }cm=23.50\text{ }cm$.

2. Find the perimeter of the following triangle.

(a) 14.7 cm                    (b) 13.2 cm

(c) 13.2 c m                   (d) 16.5 cm

(e) None of these

Solution: Perimeter of the triangle PQR

$=4\text{ }cm+4.7\text{ }cm+6\text{ }cm$

$=14.7\text{ }cm$

3. Find the perimeter of the following quadrilateral.

(a) 12 cm                                   (b) 10 cm

(c) 15 cm                                   (d) 19 cm

(e) None of these

Solution: Perimeter of the quadrilateral $=PS+SR+RQ+QP=5\text{ }cm+3\text{ }cm+4\text{ }cm+3cm=15\text{ }cm$

4. Find the perimeter of the rectangle whose length is 12 cm and breadth is 8 cm.

(a) 40 cm                      (b) 20 cm

(c) 15 cm                      (d) 30 cm

(e) None of these

Solution: Perimeter of the rectangle

$=2\left( 12+8 \right)=40\text{ }cm$.

5. Find the perimeter of the square whose length of one side is 9 cm.

(a) 32 cm                      (b) 31 cm

(c) 36 cm                      (d) 15 cm

(e) None of these

Solution: Perimeter of a square $=4~\times \,side$

$=4~\times \,9\text{ }cm=36\text{ }cm$

6. If radius of a circle is 0.35 cm, find the perimeter of the circle.

(a) 2.2 cm                                  (b) 2.1 cm

(c) 2.3 cm                                  (d) 3.1 cm

(e) None of these

Solution: Perimeter the circle $=2\pi r$

$=2\times \frac{22}{7}\times 0.35\,\,cm$

$=2.2\text{ }cm$

7. Find the area of the triangle whose base is 75 cm and height is 80 cm.

(a) $3000\,c{{m}^{2}}$

(b) $1500\,c{{m}^{2}}$

(c) $3500\,c{{m}^{2}}$

(d) $2000\,c{{m}^{2}}$

(e) None of these

Solution: Area of the triangle $=1/2~\times \,b~\times \,h$

$=\frac{1}{2}\times ~75\text{ }cm~\times \,80\text{ }cm=3000\text{ }c{{m}^{2}}$

8. Find the area of the rectangle whose length is 17 cm and breadth is 15 cm.

(a) $253\,c{{m}^{2}}$

(b) $255\,c{{m}^{2}}$

(c) $241\text{ }c{{m}^{2}}$

(d) $234\text{ }c{{m}^{2}}$

(e) None of these

Solution: Area of the rectangle $\text{=l }\!\!~\!\!\text{ }\!\!\times\!\!\text{ }\,\text{b}$

$=17\text{ }cm~\times \,15\text{ }cm=255\text{ }c{{m}^{2}}$

9. Find the area of the square whose length of each side is 21 cm.

(a) $441\,c{{m}^{2}}$

(b) $420\,c{{m}^{2}}$

(c) $244\,c{{m}^{2}}$

(d) $211\,c{{m}^{2}}$

(e) None of these

Solution: Area of the square $\text{=side }\!\!\times\!\!\text{ side=21 cm }\!\!~\!\!\text{ }\!\!\times\!\!\text{ }\,\text{21 cm=441 c}{{\text{m}}^{\text{2}}}$

10. Find the area of the circle whose radius is 0.28 cm.

(a) $0.2342\,c{{m}^{2}}$

(b) $0.2251\,c{{m}^{2}}$

(c) $0.2464\,c{{m}^{2}}$

(d) $0.2142\,c{{m}^{2}}$

(e) None of these

Solution: Area of a circle $=2{{r}^{2}}$

$=\frac{22}{7}\times ~0.28\text{ }cm~\times \,0.28\text{ }cm=0.2464\text{ }c{{m}^{2}}$

11. Find the volume of the cuboid whose length, breadth and height are 15 cm, 13 cm and 14 cm respectively.

(a) $2507\,c{{m}^{2}}$

(b) $2730\,\,c{{m}^{2}}$

(c) $2302\,c{{m}^{2}}$

(d) $2350\,\,c{{m}^{2}}$

(e) None of these

Solution: Volume of the cuboid $\text{=l }\!\!~\!\!\text{ }\!\!\times\!\!\text{ }\,\text{b }\!\!~\!\!\text{ }\!\!\times\!\!\text{ }\,\text{h}$

$=15\text{ }cm~\,\times \,13\text{ }cm\times 14\text{ }cm=2730\text{ }c{{m}^{3}}$

Volume

In our daily life a number of things are stored in different kinds of containers Holding capacity of a container is called its volume.

Volume of a Cuboid

Volume of a cuboid = length $\times$ breadth $\times$ height = Ibh.

Volume of the cuboid$ABCDEFG=AB\times AE\times BC$.

Where, length = AB, breadth = AE and height = BC

Volume of a Cube

Volume of a cube $=sid{{e}^{3}}=side~\times \,side~\times \,side$

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