Question

Perpendicular sides of a right angled triangle are 12 and 16 cm. What is the area of a

semicircle drawn with the hypotenuse as the diameter?

(a) 314

(b) 154

(c) 616

(d) 100
please answer the question fast with explaination!!!!!!!!!

Answer 1

Answer:

157 cm²

Step-by-step explanation:

Find the length of the hypotenuse:

a² + b² = c²

12² + 16² = c²

c² = 400

c = √400

c = 20 cm

Find the diameter:

Diameter = Length of hypotenuse

Diameter = 20 cm

Find the radius:

Radius = Diameter ÷ 2

Radius = 20 ÷ 2

Radius = 10 cm

Find the area of the circle:

Area = πr²

Area = π(10)²

Area = 100π = 314 cm²

Find the area of the semicircle:

Area of the semicircle = 314 ÷ 2 = 157 cm²

Answer: Area of the semicircle = 157 cm²

* Unless the question is asking for area of the circle which will then be (A) 314.

Answer 2

Find the length of the hypotenuse:

a² + b² = c²

12² + 16² = c²

c² = 400

c = √400

c = 20 cm

Find the diameter:

Diameter = Length of hypotenuse

Diameter = 20 cm

Find the radius:

Radius = Diameter ÷ 2

Radius = 20 ÷ 2

Radius = 10 cm

Find the area of the circle:

Area = πr²

Area = π(10)²

Area = 100π = 314 cm²

Find the area of the semicircle:

Area of the semicircle = 314 ÷ 2 = 157 cm²

Answer: Area of the semicircle = 157 cm²

* Unless the question is asking for area of the circle which will then be (A) 314.