Question

Can someone help me to understand this? Math 20 points

Answer 1

Given:

A triangle is placed in a semicircle with a radius of 6 cm.

We need to determine the area of the shaded region.

Area of the triangle:

The area of the triangle can be determined using the formula,

$A=\frac{1}{2} bh$

Substituting b = 6 and h = 6, we get;

$A=\frac{1}{2}(6)(6)$

$A=\frac{1}{2}(36)$

$A=18$

Thus, the area of the triangle is 18 cm²

Area of the semicircle:

The area of the semicircle can be determined using the formula,

$A=\frac{\pi r^2}{2}$

Substituting π = 3.14 and r = 6, we get;

$A=\frac{(3.14)(6)^2}{2}$

$A=\frac{113.04}{2}$

$A=56.52$

Thus, the area of the semicircle is 56.52 cm²

Area of the shaded region:

The area of the shaded region can be determined by subtracting the area of the triangle from the area of the semicircle.

Thus, we have;

Area = Area of semicircle - Area of triangle

Substituting the values, we get;

$Area = 56.52-18$

$Area = 38.52$

Thus, the area of the shaded region is 38.52 cm²

Answer 2

Answer:

20.52 cm²

Step-by-step explanation:

Semicircle - triangle

(½ pi × 6²) - (½ × 12 × 6)

(½ × 3.14 × 36) - 36

20.52