Question

A triangle is placed in a semicircle with a radius of 5cm, as shown below. Find the area of the shaded region

Answer 1

Use 3.14 as π and don't round? Using 3.14 as π is rounding!

The semicircle has area πr²/2, half the circle area, so for r=5 that's (25/2)π.

The triangle has base 10 and height 5 so area 25.

The shaded area is the difference

A = (25/2)π - 25 = 25(π/2 - 1)

Setting π=3.14

A = 25(3.14/2 - 1) = 14.25

Answer: 14.25 sq cm

Answer 2

The answer to your question is Shaded area = 14.25 cm²

Explanation:

Data

radius = 5 cm

π = 3.14

Process

1) Find the area of the semicircle

Area = πr²/2

-Substitution

Area = (3.14)(5)²/2

-Simplification

Area = 39.25 cm²

2.- Find the area of the triangle

Area = base x height / 2

-Substitution

Area = (10 x 5) /2

-Simplification

Area = 50 / 2

-Result

Area = 25 cm²

3.-Calculate the area of the shaded region

Shaded area = Area of the semicircle - Area of the triangle

Shaded area = 39.25 cm² - 25 cm²

= 14.25 cm²