Chapter 11, Problem 41SGR

To determine

To calculate the area of museum.

Answer to Problem 41SGR

  $14057.14f{t}^2$

Explanation of Solution

Given Information: $60ft,20ft.$

Formula Used:Area of circle = $\pi \times r^2$ , Area of square = ${(Side)}^2$ & Area of rectangle = $Length\times Breadth$

Calculation:

In given figure, it shows 1 square, 4 rectangle and 4 semi-circle.

So, Area of museum= Area of square + Area of 4 rectangle + Area of 4 semi-circle.

So, first calculate area of square.

Area of square = ${(Side)}^2$

As Side = 60 ft.

Area of square = ${(60)}^{2}f{t}^2$

Area of square= $3600f{t}^2$

Now, calculate area of rectangle = $Length\times Breadth$

Length = 60 ft. and Breadth = 20 ft.

Area of rectangle = $60\times 20f{t}^2$

Area of rectangle = $1200f{t}^2$

Hence, for calculate area of 4 rectangular

Area of 1 rectangle = $1200f{t}^2$

Area of 4 rectangle = $1200\times 4f{t}^2$

Area of 4 rectangle = $4800f{t}^2$

Now, calculate area of semi-circle = $\frac{\pi \times r^2}{2}$

Radius = r.

Area of semi-circle = $\frac{\pi \times r^2}{2}$

Now, radius is of 30 ft.

Area of semi-circle = $\frac{\pi \times {30}^2}{2}f{t}^2$

Now, $\pi =\frac{22}{7}$

Area of semi-circle = $\frac{22}{7}\times \frac{30\times 30}{2}f{t}^2$

Area of semi-circle = $1414.29f{t}^2$

Hence, for calculate area of 4 semi-circle

Area of 1 semi-circle = $1414.29f{t}^2$

Area of 4 semi-circle = $1414.29\times 4f{t}^2$

Area of 4 semi-circle = $5657.14f{t}^2$

Area of museum = Area of square + Area of 4 rectangle + Area of 4 semi-circle

Area of museum= $3600f{t}^2+4800f{t}^2+5657.14f{t}^2$

Area of museum= $14057.14f{t}^2$