Question

In parallelogram ABCD, CD = 10 cm. Given that area of $△$BCE is 15 $c{m}^2$ and CF = 5 cm, then find the area of trapezium AECD.

• A. 30 $c{m}^2$
• B. 48 $c{m}^2$
• C. 65 $c{m}^2$
• D. 78 $c{m}^2$

Answer 1

The correct option is C 65 $c{m}^2$

As ABCD is parallelogram, AB=CD = 10 cm

Area of triangle = $\frac{1}{2}$$\times$base$\times$height
Area of $△$BCE = $\frac{1}{2}$$\times$BE$\times$CF
15 =$\frac{1}{2}$$\times$BE$\times$5
BE = $\frac{15\times 2}{5}$ = $\frac{30}{5}$ = 6 cm

AE = AB+BE = 10+6 = 16 cm

Area of trapezium ADCE
= $\frac{1}{2}$$\times$(Sum of parallel sides)$\times$height
= $\frac{1}{2}$$\times$(CD+AE)$\times$CF
= $\frac{1}{2}$$\times$(10+16)$\times$5
= $\frac{1}{2}$$\times$26$\times$5 = 13$\times$5 = 65 $c{m}^2$