Answer:
[tex]Area = 64 + 16\pi[/tex]
Step-by-step 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:
[tex]s = 8in[/tex] --- length of the square
[tex]d = 8in[/tex] --- diameter of each semicircle
Calculate radius
[tex]r = 0.5 * d[/tex]
[tex]r = 0.5 * 8 = 4in[/tex]
The area of the square is:
[tex]Area = Length^2[/tex]
[tex]A_1 = 8^2[/tex]
[tex]A_1 = 64in^2[/tex]
The area of the two semicircles is:
[tex]A_2 =2 * \frac{\pi r^2}{2}[/tex] i.e. 2 multiplied by the area of 1
[tex]A_2 = \pi r^2[/tex]
[tex]A_2 = \pi *4^2[/tex]
[tex]A_2 = \pi *16[/tex]
[tex]A_2 = 16\pi[/tex]
So, the area of the heart is:
[tex]Area = A_1 + A_2[/tex]
[tex]Area = 64 + 16\pi[/tex]
