Answer:
31.63 feet^2
Explanation:
We are finding the areas of each and every individual geometric shape that makes up this composite figure.
Let's find the area of the semi-circles.
First, we need to know the area of a circle.
A = π
Where "π" represents pi which you can use values of 22/7(closest fraction to pi) or 3.14 to make it short. Often, 3.14 is used for pi even if the instructions don't directly say it. 22/7 is not commonly used because it isn't completely accurate.
"R" represents the radius, which is the length of a line from the center/exact middle to the edge/circumference of a circle. A better idea of circumference is if you picture any other 2D figure and it's perimeter.
Since we are given two semi-circles and a diameter, the first thing we'll need to do is find the radius.
The diameter is double of the radius. It is a full line connecting from one edge/circumference of a circle to the other edge/circumference crossing through the center/middle of the circle.
The diameter "5 feet" is stated, so in order to determine the radius, we'll have to half the value of the diameter to get the radius. In other words, we divide 5 by 2 to get the radius (again, half the diameter).
So,
5/2 = 2.5 feet
Now that we've found the radius, let's plug it in the full circle's area formula. However, we are given two semi-circles. Even though we are given two semi-circles, the measurements (aka the diameter) remains the same in both semi-circles. Therefore, both these semi-circles combined form to make a full circle.
Next, let's plug the value that we have into the formula for the area of a full circle:
A = π
A = π(2.5)^2
(the ^ sign indicates that the base 5, is raised to the power of 2- aka squaring).
Solve exponents first according to PEMDAS:
A = π(6.25)
Substitute π for 3.14- I prefer to use 3.14 since it's the simplest way to use pi:
A = 3.14(6.25)
A = 19.625 feet^2 is the area of these two semi-circles combined.
Now, let's find the area of the triangle.
First, we need to find out what the formula for the area of a triangle is:
A = 1/2BH
Where "B" represents the base of a triangle and "H" represents the height.
The height of a triangle is usually indicated by a line that crosses through the middle of it.
We are given values of:
Height = 4
Base = 6
Let's plug these values into our formula:
A = 1/2BH
A = 1/2(6)(4)
Solve:
A = 1/2(24)
A = 12 feet^2 is the area of the triangle.
Now, let's add the areas of all these figures together to get the total area of this figure.
19.625 + 12
= 31.625
They want us to round to the nearest hundredth, so:
31.625 rounds to 31.63.
The area of this figure is 31.63 feet^2.