Answer
Option C is correct.
Area of the figure = 50.13 inches squared
Step-by-step explanation
The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
So, we need to calculate the radius of the semicircle on top of the figure.
a = radius of the semicircle = ?
b = 12
hyp = √153
a² + b² = (hyp)²
a² + 12² = (√153)²
a² + 144 = 153
a² = 153 - 144
a² = 9
Take the square root of both sides
√a² = √9
a = 3 in.
So,
Area of the figure = (Area of triangle) + (Area of semicircle)
Area of triangle = ½bh
b = Base of the triangle = a + a = 3 + 3 = 6 in.
h = perpendicula height of the triangle = 12 in.
Area of triangle = ½bh = ½ (6) (12) = 36 square inches
Area of semi circle = ½ (Area of circle) = ½ (πr²)
r = Radius = 3 in.
Area of semi circle = ½ (πr²) = ½ (π (3²)) = 4.5π = 14.13 square inches
Area of the figure = (Area of triangle) + (Area of semicircle)
= 36 + 14.13
= 50.13 inches squared
Hope this Helps!!!