Question

A banner is made of a square and a semicircle. The square has side lengths of 22 inches. One side of the square is also the diameter of the semicircle. What is the total area of the banner? Use 3.14 for pi.

Answer 1

Given:

A banner is made of a square and a semicircle.

Side lengths of the square = 22 inches

Diameter of semicircle is equal to the side length of square.

To find:

The total area of the banner.

Solution:

We know that, the area of a square is

$Area=a^2$

Where, a is the side length of the square.

Putting a=22, we get

$A_1=(22)^2$

$A_1=484$

So, the area of the square is 484 sq. inches.

Diameter of semicircle = Side length of square = 22 inches

Radius of semicircle = 11 inches.

The area of a semicircle is:

$Area=\dfrac{1}{2}\pi r^2$

Where, r is the radius of the semicircle.

Putting r=11 and $\pi=3.14$, we get

$A_2=\dfrac{1}{2}(3.14)(11)^2$

$A_2=1.57(121)$

$A_2=189.97$

So, the area of the semicircle is 189.97 sq. inches.

Now, the total area of the banner is

$A=A_1+A_2$

$A=484+189.97$

$A=673.97$

Therefore, the total area of the banner is 673.97 sq. inches.