Question

In given figure, distance between corners of rhombus ABCD and rhombus EFGH is 2 cm. If EG and FH are 3 cm and 4 cm respectively, then find the shaded area.

Answer 1

According to given condition
AE = FB = GC = HD = 2 cm
AC = EG + AE + CG = 3 + 2 + 2 = 7 cm
BD = FH + DH + FB = 4 + 2 + 2 = 8 cm

Area of shaded region =
area of rhombus ABCD
- area of rhombus EFGH

Area of rhombus =
$\frac{1}{2}$$\times$(product of diagonals)
Area of rhombus EFGH = $\frac{1}{2}$$\times$(EG$\times$FH)
= $\frac{1}{2}$$\times$(3$\times$4) = $\frac{12}{2}$ = 6 cm${}^2$
Area of rhombus ABCD = $\frac{1}{2}$$\times$(AC$\times$BD)
= $\frac{1}{2}$$\times$(7$\times$8) = $\frac{56}{2}$ = 28 cm${}^2$

Area of shaded region= 28 - 6 = 22 $c{m}^2$