Question

In the given trapezium ABCE, perimeter of rectangle ABDE is 28 cm and its length is 8 cm and DC = 2 cm, then find the area of trapezium ABCE.

• A. 24 $c{m}^2$
• B. 48 $c{m}^2$
• C. 54 $c{m}^2$
• D. 72 $c{m}^2$

Answer 1

The correct option is C 54 $c{m}^2$

Given :
Perimeter of rectangle ABDE = 28 cm
Length = AB = DE = 8 cm
Breadth = AE = BD

Perimeter of rectangle ABDE = 28
2(Length+Breadth) = 28
2(8+Breadth) = 28
16+2(Breadth) = 28
2(Breadth) = 28 - 16 = 12
$⟹$ Breadth = AE = BD = 6 cm
BD = height of trapezium ABCE
CE = DE + DC = 8 + 2 = 10

Area of trapezium
= $\frac{1}{2}$$\times$(Sum of parallel sides)$\times$height
=$\frac{1}{2}$$\times$(CE+AB)$\times$BD
=$\frac{1}{2}$$\times$(10+8)$\times$6
=$\frac{1}{2}$$\times$18$\times$6
= 9$\times$6 = 54 $c{m}^2$