A stage is in the form of a rectangle and a semicircle as shown. Work out the total area of the stage. Give your answer correct to 2 significant figures. *
Answers
Answer:
Here is your answer
Step-by-step explanation:
Given :
- A stage is in the form of a rectangle and a semicircle as shown.
To find :
- Total area of the stage =?
Formula Used :
- Area of Rectangle = length x breadth
- Area of semi-circle = 1/2 π r²
Step-by-step explanation :
1st Case :
Length of rectangle = 16 m.
Breadth of rectangle = 5.5 m.
We know that,
Area of Rectangle = length x breadth
Substituting the values in the above formula, we get,
= 16 × 5.5
= 88
Therefore, Area of the rectangle = 88 m².
2nd Case :
In Semi - Circle,
Length of rectangle = Diameter of circle = 16 m.
So, Radius of the Circle = Diameter /2 = 16/2 = 8 m.
We know that,
Area of semi-circle = 1/2 π r²
Substituting the values in the above formula, we get,
= 1/2 × 22/7 × (8)²
= 1/2 × 3.14 × 8 × 8
= 3.14 × 32
= 100.48
= 100.48
Therefore, Area of the semicircle = 100.48 m².
Now,
Total Area of the given Figure = Area of rectangle + Area of semicircle
Substituting the values, we get,
= 88 + 100.48
= 188.48
Therefore, total area of stage = 188.48 m².
