Question

If the area of trapezium ABCE is 35 $c{m}^2$, and CE = 8 cm, AE = 5 cm, find the area of $△$BDC.

• A. 5 $c{m}^2$
• B. 6 $c{m}^2$
• C. 10 $c{m}^2$
• D. 12 $c{m}^2$

Answer 1

The correct option is A 5 $c{m}^2$

Area of triangle
= Area of trapezium ABCE
- Area of rectangle ABDE

Area of trapezium ABCE
= $\frac{1}{2}$$\times$(Sum of parallel sides)$\times$height
35 = $\frac{1}{2}$$\times$(AB+CE)$\times$AE
35 = $\frac{1}{2}$$\times$(AB+8)$\times$5
$\frac{35\times 2}{5}$ = AB+8 = 7$\times$2 = 14
AB+8 = 14
AB = 14-8 = 6 cm

Area of rectangle ABDE
= length$\times$breadth
= AB$\times$AE = 6$\times$5 = 30 $c{m}^2$

Area of triangle = 35 - 30 = 5 $c{m}^2$