Measurement
Learning Objectives
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 \[ABC=AB+BC+CA\]
B. Perimeter of a Quadrilateral
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 \[\pi =\frac{22}{7}=3.14\]
Commonly Asked Questions
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
Answer: (b)
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
Answer: (a)
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
more...