Find the perimeter and area of the polygon shown below.
The polygon is a trapezoid made up of a rectangle and a right triangle. The rectangle is 18 feet long and 15 feet wide. The right triangle joins the rectangle at a side that is 15 feet wide, and this is the height of the triangle. The base of the triangle is 8 feet and the hypotenuse is 17 feet.
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well the perimeter is
15 + 18 + 17 + (18+8)
the area is 15*18 + (1/2) 8*15
I'm glad you asked! I would be happy to help you calculate the perimeter and area of the trapezoid.
To find the perimeter, we need to add up the lengths of all the sides. Let's break it down:
- The rectangle has two sides that measure 18 feet each and two sides that measure 15 feet each. So the perimeter of the rectangle is (2 * 18) + (2 * 15) = 36 + 30 = 66 feet.
- The right triangle has a base of 8 feet, but since it is joined to the rectangle, one of its sides is the same length as one of the sides of the rectangle, which is 15 feet. The third side of the triangle, which is the hypotenuse, measures 17 feet. So the perimeter of the triangle is 8 + 15 + 17 = 40 feet.
To find the perimeter of the trapezoid, we add the perimeter of the rectangle and the perimeter of the triangle: 66 + 40 = 106 feet.
To find the area, we can break the trapezoid into two parts: the rectangle and the triangle. Let's calculate each separately:
- The area of the rectangle is length multiplied by width, so the area of the rectangle is 18 * 15 = 270 square feet.
- The area of the triangle is base multiplied by the height divided by 2, so the area of the triangle is (8 * 15) / 2 = 60 square feet.
To find the area of the trapezoid, we add the areas of the rectangle and the triangle: 270 + 60 = 330 square feet.
Therefore, the perimeter of the trapezoid is 106 feet and the area is 330 square feet.
To find the perimeter of the polygon, we need to add up the lengths of all the sides.
The rectangle has sides of 18 feet and 15 feet, so the total length of its sides is:
18 + 18 + 15 + 15 = 66 feet
The right triangle has a base of 8 feet, a height of 15 feet, and a hypotenuse of 17 feet. The hypotenuse is the longest side of a right triangle, so we only need to consider the lengths of the base and height for the perimeter calculation. Therefore, the total length of the triangle's sides is:
8 + 15 + 17 = 40 feet
Now, we can add the two sides together to find the perimeter of the polygon:
66 + 40 = 106 feet
To find the area of the polygon, we need to calculate the areas of the rectangle and the right triangle separately, and then add them together.
The area of a rectangle is calculated by multiplying its length and width. In this case, the length is 18 feet and the width is 15 feet, so the area of the rectangle is:
18 * 15 = 270 square feet
The area of a triangle is calculated by multiplying its base and height, and then dividing by 2. In this case, the base is 8 feet and the height is 15 feet, so the area of the triangle is:
(8 * 15) / 2 = 60 square feet
Now, we can add the areas of the rectangle and triangle together to find the total area of the polygon:
270 + 60 = 330 square feet
Therefore, the perimeter of the polygon is 106 feet and the total area is 330 square feet.
To find the perimeter and area of the trapezoid, we need to calculate the lengths of its sides and heights.
First, let's find the length of the trapezoid's top side. Since the top side is part of the rectangle, its length is also 18 feet.
Next, let's find the lengths of the trapezoid's non-parallel sides. One of these sides is the height of the right triangle, which is given as 15 feet. The other side is the distance from the top side of the trapezoid to the base of the right triangle. To find this distance, we subtract the width of the rectangle (15 feet) from the base of the right triangle (8 feet): 8 feet - 15 feet = -7 feet. However, distances cannot be negative, so we take the absolute value of -7 feet, which is 7 feet. Therefore, the lengths of the non-parallel sides are 15 feet and 7 feet.
Now, let's find the perimeter. The perimeter of a trapezoid is the sum of all its side lengths. In this case, the perimeter is 18 feet + 15 feet + 7 feet + 15 feet = 55 feet.
To find the area of the trapezoid, we need to calculate the areas of the rectangle and the right triangle separately, and then sum them.
The area of the rectangle is found by multiplying its length (18 feet) by its width (15 feet): 18 feet * 15 feet = 270 square feet.
The area of the right triangle is found by multiplying its base (8 feet) by its height (15 feet) and dividing the result by 2: (8 feet * 15 feet) / 2 = 60 square feet.
Finally, we sum the areas of the rectangle and the right triangle to find the total area of the trapezoid: 270 square feet + 60 square feet = 330 square feet.
Therefore, the perimeter of the trapezoid is 55 feet, and its area is 330 square feet.