Question

a semicircular archway is built in front of a garden using 8 congruent granite tiles, as shown in the diagram.
find the area of one of the tiles. use 3.14 for π.
remember that a semi - circle is half of a circle.
the area of one tile is square feet.

Explanation:

Step1: Calculate the area of the larger semi - circle

The formula for the area of a circle is \(A = \pi r^{2}\), and for a semi - circle it is \(A=\frac{1}{2}\pi r^{2}\). The radius of the larger semi - circle \(R=12 + 2=14\) ft.
The area of the larger semi - circle \(A_{1}=\frac{1}{2}\times3.14\times14^{2}=\frac{1}{2}\times3.14\times196 = 307.72\) square feet.

Step2: Calculate the area of the smaller semi - circle

The radius of the smaller semi - circle \(r = 12\) ft.
The area of the smaller semi - circle \(A_{2}=\frac{1}{2}\times3.14\times12^{2}=\frac{1}{2}\times3.14\times144=226.08\) square feet.

Step3: Calculate the area of the ring - shaped semi - circle (one tile)

The area of the ring - shaped semi - circle (one tile) \(A=A_{1}-A_{2}\).
\(A = 307.72-226.08=81.64\) square feet.

Answer:

\(81.64\)