Question

Karla discovered that she could create the perfect shaped heart by combining two semicirlcles and a square what is the area of he heart karla created

Answer 1

`Area = 64 + 16\pi`

Explanation:

Given

See attachment for the heart created

Required

The area of the heart

The area of the heart is the sum of the area of the square and the areas of the two semicircles.

From the attachment, we have:

`s = 8in` --- length of the square

`d = 8in` --- diameter of each semicircle

Calculate radius

`r = 0.5 * d`

`r = 0.5 * 8 = 4in`

The area of the square is:

`Area = Length^2`

`A_1 = 8^2`

`A_1 = 64in^2`

The area of the two semicircles is:

`A_2 =2 * (\pi r^2)/(2)` i.e. 2 multiplied by the area of 1

`A_2 = \pi r^2`

`A_2 = \pi *4^2`

`A_2 = \pi *16`

`A_2 = 16\pi`

So, the area of the heart is:

`Area = A_1 + A_2`

`Area = 64 + 16\pi`