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,
[tex]A=\frac{1}{2} bh[/tex]
Substituting b = 6 and h = 6, we get;
[tex]A=\frac{1}{2}(6)(6)[/tex]
[tex]A=\frac{1}{2}(36)[/tex]
[tex]A=18[/tex]
Thus, the area of the triangle is 18 cm²
Area of the semicircle:
The area of the semicircle can be determined using the formula,
[tex]A=\frac{\pi r^2}{2}[/tex]
Substituting π = 3.14 and r = 6, we get;
[tex]A=\frac{(3.14)(6)^2}{2}[/tex]
[tex]A=\frac{113.04}{2}[/tex]
[tex]A=56.52[/tex]
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;
[tex]Area = 56.52-18[/tex]
[tex]Area = 38.52[/tex]
Thus, the area of the shaded region is 38.52 cm²
