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. round to the nearest tenth.

Answer 1

Given: 
8 tiles
radius from the center of the archway to the inner edge of the tile. 7 ft.
radius from the center of the archway to the outer edge of the tile. 8 ft = 7 ft + 1 ft.

Area of a semi circle = π r² / 2 
A = (3.14 * (7ft)²) / 2 = (3.14 * 49ft²) / 2 = 153.86 ft² / 2 = 76.93 ft²
A = (3.14 * (8ft)²) / 2 = (3.14 * 64ft²) / 2 = 200.96 ft² / 2 = 100.48 ft²

100.48 ft² - 76.93 ft² = 23.55 ft²
23.55 ft² / 8 tiles = 2.94 ft² per tile.