Question

Find the area of the shaded region. Round to the nearest hundredth where necessary. Remember: you are subtracting the areas.

Answer 1

Given:

The base of the given figure = 23.8 ft

Height of the parallelogram = 15 ft

To find the area of the shaded region.

Formula

• $A = A_{1} -A_{2}$

where, $A$ be the area of the shaded region

$A_{1}$ be the area of the parallelogram.

$A_{2}$ be the area of the triangular part.

• The area of triangle $A_{2} = \frac{1}{2} bh$ where, b be the base and h be the height.

• The area of the parallelogram $A_{1} =( base)(height)$

• By Pythagoras theorem, $hypotenuse^{2} = base^{2}+height^{2}$

Now,

Putting, Base = 21, Hypotenuse = 23.8 we get,

$Height^{2} = 23.8^{2}-21^{2}$

or, $Height = \sqrt{566.44-441}$

or, $Height = 11.2$

Therefore,

Area of the parallelogram $A_{1} = (23.8)(15)$ sq ft = 357 sq ft

Area of the triangle $A_{2}$ = $\frac{1}{2}(11.2)(21)$ sq ft = 117.6 sq ft

So,

The area of the shaded part = (357-117.6) sq ft = 239.4 sq ft

Hence,

The area of the shaded part is 239.4 sq ft.