Question

Find the area of given figures, if HI = 6, GF = 7, CD = 8, AB = 11, JF = DE = BC = CG = 2, GH = 4 in cm.

• A. 45 $c{m}^2$
• B. 54 $c{m}^2$
• C. 66 $c{m}^2$
• D. 78 $c{m}^2$

Answer 1

The correct option is C 66 $c{m}^2$

CE = CD+DE = 8+2 = 10 cm
GJ = GF+JF = 7+2 = 9 cm

Area of figure =
Area of trapezium ABCD
+ Area of trapezium CEFG
+ Area of trapezium GHIJ

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

Area of trapezium ABCD
= $\frac{1}{2}$$\times$(AB+CD)$\times$BC = $\frac{1}{2}$$\times$(11+8)$\times$2
= $\frac{1}{2}$$\times$19$\times$2 = 19$\times$1 = 19 $c{m}^2$

Area of trapezium CEFG
= $\frac{1}{2}$$\times$(CE+GF)$\times$CG = $\frac{1}{2}$$\times$(10+7)$\times$2
= $\frac{1}{2}$$\times$17$\times$2 = 17$\times$1 = 17 $c{m}^2$

Area of trapezium GHIJ
= $\frac{1}{2}$$\times$(GJ+HI)$\times$GH = $\frac{1}{2}$$\times$(9+6)$\times$4
= $\frac{1}{2}$$\times$15$\times$4 = 15$\times$2 = 30 $c{m}^2$

Area of figure = 19+17+30 = 66 $c{m}^2$