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

Answer:

$123.44 inches^2$

Step-by-step explanation:

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

$A=2* \frac{1}{2} \pi r_{semicircle}^2+\frac{1}{4}\pi r_{quartercircle}^2$

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.

$A=2* \frac{1}{2} \pi(6.1)^2+\frac{1}{4}\pi (2.9)^2$

Substitute our values of pi for 3.14

$A=2* \frac{1}{2} (3.14)(6.1)^2+\frac{1}{4}(3.14)(2.9)^2$

Simplify

$A=(3.14)((6.1)^2+\frac{1}{4}(2.9)^2)$

Now solve for A

$A=123.44$