To calculate the area of the patio.
Answer to Problem 27STP
Explanation of Solution
Given information:
The figure consists of a rectangle and a semicircle. Once the 4 feet wide patio is removed, there would be another set of rectangle and semicircle.
For this sake of calculation, the details of both the sets of rectangle and semicircle is mentioned.
Outer rectangle has length
Outer semicircle has diameter
Inner rectangle has length
Inner semicircle has diameter
Formula used: Area of outer inner and rectangle
Area of outer and inner semicircle
For calculations,
Calculation:
To calculate area of the patio, calculate the area of the outer region and subtract the inner region from it. Effectively, 4 feet will be removed from all dimensions while calculating the inner portion.
Both parts have a rectangle and semicircle. This would be found out by adding the areas of the rectangle and semicircle.
Area of outer region.
Area of the outer rectangle’s formula.
Applying values in the formula.
Area of the outer semi-circle.
Formula for area of outer semicircle.
Putting the values in the formula.
Simplifying the same.
Now, area of the outer region
Add the areas of the outer portion
Numeric values of the respective shapes.
Area of inner region.
Area of the inner rectangle’s formula.
Applying values in the formula.
Area of the inner semi-circle.
Formula for area of inner semicircle.
Putting the values in the formula.
Simplifying the same.
Now, area of the inner region
Add the areas of the outer portion
Numeric values of the respective shapes.
Area of the patio would be the difference between the areas of the outer and inner regions.
This is given by.
Areas of the two regions.
Subtracting the same.
Rounding off to the nearest tenth.
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