Question

A decorative​ tile, like the one shown​ (which is not to​ scale) features an image meant to resemble a butterfly. The wings are two​ semicircles, each with radius 6.1 inches. The head is a quarter circle with radius 2.9 inches. What is the total area of the butterfly image on the​ tile? Use 3.14 for pi.

Answer 1

`123.44 inches^2`

Explanation:

Total area = 2 x semi-circle + quarter-circle

`A=2* (1)/(2) \pi r_(semicircle)^2+(1)/(4)\pi r_(quartercircle)^2`

The area of a circle is
`\pi r ^2`, so the area of half a circle is half this, and the area of quarter of a circle is a quarter of this.

`A=2* (1)/(2) \pi(6.1)^2+(1)/(4)\pi (2.9)^2`

Substitute our values of pi for 3.14

`A=2* (1)/(2) (3.14)(6.1)^2+(1)/(4)(3.14)(2.9)^2`

Simplify

`A=(3.14)((6.1)^2+(1)/(4)(2.9)^2)`

Now solve for A

`A=123.44`