Question

A trapezium has parallel sides 15 cm and 22 cm.
The perpendicular distance between the two parallel
sides is 9 cm.
Find the area of the trapezium.​

Answer 1

Given :

• Parallel sides of a trapezium = 15 cm and 22 cm

• Perpendicular distance between the two parallel sides = 9 cm

To find :

• Area of trapezium

Knowledge Required :-

Formula to calculate area of trapezium :-

→ Area of trapezium = ½ × Sum of parallel sides × Height of trapezium

The commonly used units for area are cm², m².

Figure :

$\setlength{\unitlength}{1.5cm}\begin{picture}\thicklines\qbezier(0,0)(0,0)(1,2.2)\qbezier(0,0)(0,0)(4,0)\qbezier(3,2.2)(4,0)(4,0)\qbezier(1.5,2.2)(0,2.2)(3,2.2)\put(0.8,2.4){ \bf A }\put(3,2.4){ \bf D }\put(-0.3,-0.3){ \bf B }\put(4,-0.3){ \bf C }\put(4.4,0){\vector(0,0){2.2}}\put( 4.4, 0){\vector(0,-1){0.1}}\put(4.6,1){ \bf 9\ cm }\put(0, -0.5){\vector(1,0){4}}\put(0, -0.5){\vector( - 1, 0){0.1}}\put(1.7, - 0.9){ \bf 22\ cm }\put(0.8, 2.8){\vector(1,0){2.5}}\put(0.8, 2.8){\vector( - 1, 0){0.1}}\put(1.7, 3){ \bf 15\ cm }\end{picture}$

Solution :

Substituting the given values in the formula of area of trapezium :-

→ Area of trapezium = ½ × (15 + 22) × 9

→ Area of trapezium = ½ × 37 × 9

→ Area of trapezium = 333/2

→ Area of trapezium = 166.5

Therefore, area of trapezium = 166.5 cm²