when i use "pi," im talking about the greek letter which you might have to write as π, or use in a calculator when entering an answer
all of the answers are underlined after each explanation :)
Question 1:
Area:
The picture shown splits the image into 2 half circles and two triangles. When finding the area, you can look at the two halves as one whole. The area of a circle is calculated by putting the radius to the power of two and multiplying by pi. The picture gives you the diameter, which is 5 feet. The diameter of a circle is twice the radius, so divide 5 by 2, square that number, and multiply by pi to find the area of one whole circle:
- (5/2)^2*pi
- 2.5^2*pi
- 2.5*2.5*pi
- 6.25*pi
Now we need to find the area of the two triangles. Like the circles, these two triangles make up one whole triangle. The base of the triangle is given: 6 feet. The height of this triangle is also given as 4 feet. The formula for the area of a triangle is base*height/2, so multiply 4 by 6 and divide by 2:
- 4*6/2
- 24/2
- 12
These shapes add up to make the entire figure, so the area will be
<u>12+6.25pi</u>
Perimeter:
To find the perimeter, we need to look at the problem similarly. The perimeter can be thought of as the length around a figure. The formula for the perimeter of a circle, called the circumference, is diameter*pi, so multiply the diameter, 5, by pi to find the distance around the rounded parts of the figure
- 5*pi
After finding the length around the rounded part, we need the length of the straight part, which is given to us as 6 feet. To find the total perimeter, add up the distances around each part:
<u>6+5pi</u>
Question 2:
Area:
For this question, we need to use the same base*height/2 formula to find the area of the small triangle. At first glance, the base is not obvious. Look on the right side of the rectangle. Notice how it lines up with the right side of the triangle? This side is the base, and it is given as 6 meters. The height is given as 4 meters. Usually you would think of height as how tall something is, but in triangles, a height is a line that will form a 90 degree angle with a base. Multiply 6 and 4, then divide by 2:
- 6*4/2
- 24/2
- 12
Now we need find the area of the rectangle next to the small triangle. The formula for the area of a rectangle is length*width. The length and the width are given as 10 and 6, so multiply 10 and 6:
- 10*6
- 60
Finally, add the areas of the triangle and the rectangle:
60+12=<u>72</u>
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Perimeter:
Add up the lengths around the figure- they are already given:
5+5+10+10+6=<u>36</u>
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Question 3:
Area:
This figure is made up of two shapes: A square, and a semicircle, or half circle. Since it is half of a circle, we need to calculate the area of a circle, and divide by two. The problem gives us a diameter of 6, which we know we must divide by two because a diameter is twice the size of the radius, and the formula is radius^2*pi. Divide 6 by 2:
- 6/2
- 3
Plug three into the area formula:
- 3^2*pi
- 9*pi
Divide by two because it is a half circle and has half the area:
- 9*pi/2
- 4.5*pi
Multiply the length and width of the square to find its area:
- 2*2
- 4
Now add the areas of the two parts together:
<u>4+4.5pi</u>
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Perimeter:
For the perimeter of the rounded part, use the diameter*pi formula and also divide by 2 because it is a semicircle:
- 6*pi/2
- 3*pi
The semicircle also has a bottom that is part of the perimeter and it is 6 millimeters. Add that to 3*pi:
- 3*pi+6
In a square, all sides are equal, so since one side is 2 millimeters, all four sides are 2 millimeters. Multiply 2 by 4:
- 2*4
- 8
Add these perimeters together:
- 8+3*pi+6
- 14+3*pi
We're almost done now. Notice how one side of the square is hidden and 2 millimeters of the bottom of the semicircle are hidden? This means that we need to subtract 4 before getting a final answer:
14+3*pi-4=<u>10*3pi</u>
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please let me know if anything is incorrect or hard to understand, hope this helps!!