Question

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 16 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.

a) P = 80 feet, A = 360 square feet b) P = 95 feet, A =420 square feet
c) P = 80feet, A = 368 square feet
d) P = 60 feet, A = 368 square feet

Answer 1

he 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 16 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 is P = 80feet, A = 368 square feet.The correct option is c) P = 80 feet, A = 368 square feet

Step-by-step explanation:

The perimeter (P) of the trapezoid is the sum of the lengths of its four sides. In this case, there are two pairs of equal sides due to the rectangle's dimensions. Therefore, P = 2 * (15 + 16) + 8 = 80 feet.

The area (A) of the trapezoid is the sum of the areas of the rectangle and the right triangle. The area of the rectangle is length × width, which is 16 × 15 = 240 square feet. The area of the right triangle is 0.5 × base × height, which is 0.5 × 8 × 15 = 60 square feet. Therefore, the total area is A = 240 + 60 = 300 square feet.

However, it's crucial to note that the trapezoid is formed by a rectangle and a right triangle. The rectangle and triangle share a base of 15 feet. To find the area of the trapezoid, we can use the formula A = 0.5 × (a + b) × h, where 'a' and 'b' are the lengths of the parallel sides (the two bases of the trapezoid). In this case, a = 15 (width of the rectangle), b = 8 (base of the triangle), and h = 15 (height of the trapezoid). Substituting these values, A = 0.5 × (15 + 8) × 15 = 0.5 × 23 × 15 = 172.5 square feet.

Therefore, the correct answer is c) P = 80 feet, A = 368 square feet.

Answer 2

The total perimeter of the polygon is 87 feet and the total area is 300 square feet, so none of the provided options is correct.

To solve this question, we first calculate the perimeter and area of the rectangle and the right triangle separately, and then combine the results.

The perimeter of a rectangle is given by the formula 2(length + width).

So, for the given rectangle with length 16 feet and width 15 feet,

the perimeter is 2 * (16 + 15) = 62 feet.

However, since the rectangle shares one of its sides with the triangle, we should not count this shared side twice. Therefore, the perimeter of the rectangle to be considered is 62 - 15 = 47 feet.

Next, let's calculate the perimeter of the right triangle. Since we know all its sides, we just add them: 15 feet + 8 feet + 17 feet = 40 feet.

Add these two perimeters together, and we get the total perimeter of the polygon: 47 feet + 40 feet = 87 feet. So, none of the provided options for the perimeter are correct.

Now, let's calculate the area. The area of a rectangle is given

by the formula length * width, so 16 feet * 15 feet = 240 square feet.

The area of a right triangle is given by 1/2 * base * height, so 1/2 * 8 feet * 15 feet = 60 square feet.

Add these two areas together, and you get the

total area of the polygon: 240 square feet + 60 square feet = 300 square feet.