Question

For the figures below, assume they are made of semicircles, quarter circles, and squares. For each shape, find the area and perimeter. Give your answer as a completely simplified exact value in terms of π (no approximations).

Answer 1

The perimeter is = 6(1 + √2) + 3π cm.

Total area = 4.5(4 + π) cm².

Explanation:

The given figure is consists of an isosceles right triangle and a semi-circle.

Perimeter calculation :

AC is the hypotenuse and equal to =
`\sqrt{6^(2) + 6^(2)} = 6√(2)` cm.

AB = 6 cm and

Arc BC = πr = 3π {Since
`r = (BC)/(2) = (6)/(2) = 3` cm.}

Therefore, the perimeter is = 6 + 6√2 + 3π = 6(1 + √2) + 3π cm.

Area calculation :

Area of the triangle =
`(1)/(2) * 6 * 6 = 18` cm².

Area of the semi circle =
`(1)/(2)\pi r^(2) = (1)/(2)\pi (3)^(2) = 4.5\pi` cm²

Therefore, total area = 18 + 4.5π = 4.5(4 + π) cm². (Answer)