Answer:
Area of shaded region is 15.25 m
Step-by-step explanation:
Step 1 :- Finding the Diameter
As we know that length of the hypotenuse of triangle is the diameter of circle
To find length of hypotenuse using Pythagoras theorem
(a)²+(b)²= (c)²
Where, a and b is the legs and c is the length of hypotenuse of triangle.
( 8m ) ² + ( 6m ) ² = ( c ) ²
64m² + 36m² = c ²
Combine like terms
100 m² = c ²
Taking square root of each side
√100 m ² = √c²
10 m = c
Hypotenuse is the diameter of circle which is 10m.
Diameter = 10 m
Radius , r = 10 / 2 = 5 m
Step 2:- Finding the area of semi- circle
Area of semi-circle = 1 / 2 π r²
substitute the values
Area of semi-circle = 1 / 2 × π × ( 5 m )²
Evaluate the exponent
Area of semi-circle = 1 / 2 × π × 25 m²
Using value of π = 3.14
Area of semi-circle = 1 / 2 × 3.14 × 25 m²
Multiply , we get
Area of semi-circle = 39.25 m²
Step 3 :- Finding the area of triangle
Area of triangle = 1/2 × base × height
Where , base = 6 m and height = 8 m
substitute the values
Area of triangle = 1/2 × 6m × 8m
multiply,
Area of triangle = 1/ 2× 48 m²
Divide
Area of triangle = 48 m² / 2
Area of triangle = 24 m ²
Step 4 :- Area of shaded region is given by
= Area of semicircle - area of triangle
= 39.25 m² - 24 m² = 15.25 m
Hence , Area of shaded region is 15.25 m
