Answer:
The numbers correlate with the numbers that were labeled for each question
5. 243.375
4. 146.24
3. 175
Step-by-step explanation:
5.
Area of this figure would equal area of rectangle - area of 2 semi circles
Area of rectangle = length × width
Here length = 28 and width = 15
So area of rectangle = 28 × 15 = 420
Area of semi circle = 1/2(πr²)
where r = radius
Here the width of the rectangle is shared with the diamter of the semi circle meaning the diameter is the width of the rectangle, 15in.
To convert from diameter to radius we simply divide by 2 so radius = 15/2=7.5
So we have A = 1/2(πr²) and r = 7.5 and π = 3.14
==> plug in values
A = 1/2((3.14)(7.5²))
==> evaluate exponent
A = 1/2(3.14)56.25
==> multiply 3.14 and 56.25
A = 1/2(176.625)
==> divide 176.625 by 2
A = 88.3125
The area of one of the semicricles is 88.3125
There are two semi circles so we multiply that by 2
Area of both semi circles = 88.3125 × 2 = 176.625
Finally we subtract the area of the semi circles by the area of the rectangle
Area of composite figure = 420 - 176.625 = 243.375
4.
Total area = area of square + area of triangle + area of quarter circle
Area of square = s² where s = side length
The side length appears to b 8 so area of square = 8² = 64
Area of triangle = 1/2(bh) where b = base length and h = height
The base length appears to be 8 and the height is shared with the length of the square so height also = 8
We have area = 1/2(bh) and b = 8 and h = 8
So area = 1/2(8)(8)
==> multiply 8 by 8
Area = 1/2(64)
==> divide 64 by 2
Area = 32
Area of quarter circle = (1/4)πr²
where r = radius
The radius is shared with the side length of the square which has a length of 8 so radius = 8
So we have area = (1/4)πr² and we have r = 8 and π = 3.14
==> plug in values
Area = 1/4(3.14)(8²)
==> evaluate exponent
Area = 1/4(3.14)(64)
==> multiply 64 and 3.14
Area = 1/4(200.96)
==> divide 200.96 by 4
Area = 50.24
Finally we add all the areas
Total area = 50.24 + 64 + 32 = 146.24
3.
We can use a simple formula because the figure here is a trapezoid
Area of a trapezoid : [tex]A= \frac{a+b}{2} h[/tex] where a and b= base lengths and h = height
Here the base lenghts appear to be 15 and 20 and the height is 10
So we have [tex]A= \frac{a+b}{2} h[/tex] and a = 15 , b = 20 and h = 10
==> plug in values
[tex]A=\frac{15+20}{2} 10[/tex]
==> add 15 and 20
[tex]A=\frac{35}{2} 10[/tex]
==> divide 35 by 2
A = 17.5(10)
==> multiply 17.5 and 10
A = 175
And we are done!
