Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depe
find the perimeter and area of the polygon shown below.
15 ft
18 ft
←8 ft→
17 ft
options:
p = 76 feet, a = 338 square feet
p = 76 feet, a = 330 square feet
p = 91 feet, a = 390 square feet
p = 58 feet, a = 338 square feet

Explanation:

Step1: Calculate Perimeter

The polygon is a combination of a rectangle and a right triangle. The sides of the rectangle are 15 ft, 18 ft, and the triangle has a base 8 ft, hypotenuse 17 ft, and height 15 ft (since it's a right triangle with height equal to the rectangle's height). The perimeter is the sum of all outer sides: \(15 + 18 + 15 + 8 + 17\)? Wait, no. Wait, the shape: the rectangle has length 18 ft, height 15 ft. Then the triangle is attached to the right end. So the perimeter is: top side of rectangle (18 ft) + right side (triangle's hypotenuse 17 ft) + bottom side (18 + 8? No, wait, no. Wait, let's look at the diagram. The rectangle has length 18 ft, height 15 ft. Then there's a right triangle with base 8 ft, height 15 ft (so the vertical side is 15 ft, horizontal base 8 ft, hypotenuse 17 ft, which checks out: \(8^2 + 15^2 = 64 + 225 = 289 = 17^2\)). So the perimeter: left side (15 ft) + bottom (18 ft) + right side (15 ft? No, wait, the bottom is 18 ft, then the triangle's base is 8 ft, so the total bottom? Wait, no, the perimeter is the sum of all outer edges. Let's list the sides: left vertical (15 ft), bottom horizontal (18 + 8? No, wait, the rectangle's bottom is 18 ft, then the triangle's bottom is 8 ft? No, the diagram shows the rectangle with length 18 ft, then a triangle attached to the right, with base 8 ft (horizontal) and height 15 ft (vertical). So the top side of the rectangle is 18 ft, then the triangle's top side? Wait, no, the perimeter: left side (15 ft), bottom (18 ft), right side (triangle's hypotenuse 17 ft), top (18 + 8 ft? Wait, no, the top of the rectangle is 18 ft, then the triangle's top is 8 ft? Wait, no, the diagram has a right angle at the top left, so the rectangle is 18 ft (length) and 15 ft (height). Then the triangle is attached to the right end: the vertical side of the triangle is 15 ft (same as the rectangle's height), horizontal base 8 ft, hypotenuse 17 ft. So the perimeter is: left (15) + bottom (18) + right (17) + top (18 + 8) + left? Wait, no, let's count all outer sides:

- Left vertical: 15 ft
- Bottom horizontal: 18 ft
- Right vertical? No, the triangle's vertical side is internal? Wait, no, the diagram shows the rectangle with a right angle, then a dashed line (internal) and the triangle. So the outer sides are: left (15), bottom (18), right (17), top (18 + 8), and the left side? Wait, no, the top of the rectangle is 18 ft, then the triangle's top is 8 ft? Wait, no, the perimeter is the sum of all the outer edges. Let's do it step by step:

Sides:

1. Left: 15 ft

2. Bottom: 18 ft

3. Right: the hypotenuse of the triangle, 17 ft

4. Top: the length of the rectangle (18 ft) plus the base of the triangle (8 ft)? Wait, no, the top of the rectangle is 18 ft, then the triangle's top is 8 ft? Wait, no, the diagram shows the top of the rectangle is 18 ft, then a segment of 8 ft to the right, then the triangle. So the total top length is 18 + 8? No, wait, the perimeter is the sum of all the outer edges. Let's list all the outer sides:

- Left vertical: 15 ft

- Bottom horizontal: 18 ft

- Right vertical? No, the triangle's vertical side is 15 ft, but it's internal (dashed line). So the outer sides are:

Left (15), bottom (18), right (17), top (18 + 8), and the left side? Wait, no, the top is 18 ft (rectangle) plus 8 ft (triangle's base) = 26 ft? No, that can't be. Wait, maybe I'm misinterpreting. Wait, the rectangle has length 18 ft, height 15 ft. The triangle is a right triangle with legs 8 ft (horizontal) and 15 ft (vertical), hypotenuse 17 ft. So the perimeter is:

Left side: 15 ft

Bottom: 18 ft

Right side: 17 ft (hypotenuse)

Top: 18 ft (rectangle's top) + 8 ft (triangle's base) = 26 ft? Wait, no, that would be 15 + 18 + 17 + 26 = 76 ft. Ah, that matches the first option's perimeter (76 ft). So perimeter is 76 ft.

Step2: Calculate Area

The area is the area of the rectangle plus the area of the triangle.

Area of rectangle: \(length \times height = 18 \times 15 = 270\) square feet.

Area of triangle: \(\frac{1}{2} \times base \times height = \frac{1}{2} \times 8 \times 15 = 60\) square feet.

Total area: \(270 + 60 = 330\) square feet.

Answer:

\(P = 76\) feet, \(A = 330\) square feet (the second option: \(P = 76\) feet, \(A = 330\) square feet)