Answer:
The perimeter of the figure in the diagram is:
Step-by-step explanation:
To identify the perimeter of the figure shown, you must divide the figure in figures known, in this case, the top is a half of a circle, next is a rectangle, and the last could be divided into two triangles (image attached), so, we can define the perimeter of each figure identified:
1. Circle.
The circle has a diameter of 6 feet (six squares in the paper), now, you must remember that:
- PI = perimeter / diameter = 3.1416 approximately
How we know the diameter and the value of the PI, we can clear the perimeter:
- Perimeter = PI * diameter
- Perimeter = PI * 6 feet
- Perimeter = 18.849 feet
Remember this is the perimeter of a complete circle, but how we have a half circle, we must divide the perimeter obtained into 2:
- First Perimeter (a half of a circle) = 18.849 feet / 2 = 9.425 feet
2. Rectangle.
This is the easiest perimeter you can find, just need to add the 3 feet from the left side and the 3 feet from the right side, so:
- Second Perimeter (of a part of a rectangle) = 3 feet + 3 feet = 6 feet
3. Triangles.
The smallest triangle (please see the image attached) has the measures: 1 foot and 2 feet, to identify the hypotenuse you only must apply the Pythagoras theorem what is:
- Opposite leg squared + leg adjacent squared = hypotenuse squared
or
But how we need just the hypotenuse, we obtain the square root of all:
- square root (a^2 + b^2) = hypotenuse
Then we replace:
- Third perimeter = square root (1^2 ft + 2^2 ft) = 2.236 feet
And the last, for the biggest triangle, you use the same formula with square root but with the legs 5 feet and 2 feet:
- square root (a^2 + b^2) = hypotenuse
- Fourth perimeter = square root (5^2 + 2^2) = 5.385 feet
Now, you must add all the perimeters found:
- Perimeter of the figure = 9.425 feet + 6 feet + 2.236 feet + 5.385 feet
- Perimeter of the figure = 23.046 feet
