Question

Find area of shaded region if AH=ED=OP = 2 cm, AB=DC=6 cm, HG=EF=4 cm, GF=3 cm, BC=7 cm.

• A. 8 $c{m}^2$
• B. 16 $c{m}^2$
• C. 20 $c{m}^2$
• D. 30 $c{m}^2$

Answer 1

The correct option is D 30 $c{m}^2$

Area of shaded region
= Area of trapezium ABGH
+ Area of trapezium CDEF
+ Area of trapezium BCFG

Area of trapezium
= $\frac{1}{2}$$\times$(Sum of parallel sides)$\times$height

Area of shaded region
= $\frac{1}{2}$$\times$(AB+HG)$\times$AH
+ $\frac{1}{2}$$\times$(CD+EF)$\times$ED
+ $\frac{1}{2}$$\times$(BC+GF)$\times$OP

= $\frac{1}{2}$$\times$(6+4)$\times$2
+ $\frac{1}{2}$$\times$(6+4)$\times$2
+ $\frac{1}{2}$$\times$(7+3)$\times$2

= $\frac{1}{2}$$\times$10$\times$2 + $\frac{1}{2}$$\times$10$\times$2 +$\frac{1}{2}$$\times$10$\times$2
= 5$\times$2 + 5$\times$2 + 5$\times$2
= 10 + 10 + 10 = 30 $c{m}^2$