Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. find the perimeter and area of the polygon shown below.
diagram: a composite polygon with a rectangle (15 ft height, 18 ft base) and a right triangle (8 ft base segment, 17 ft hypotenuse, 15 ft height matching the rectangle).
options:

• ( p = 76 ) feet, ( a = 338 ) square feet
• ( p = 91 ) feet, ( a = 390 ) square feet
• ( p = 76 ) feet, ( a = 330 ) square feet
• ( p = 58 ) feet, ( a = 338 ) square feet

Explanation:

), and a right triangle attached to the right, so the total length of the bottom is \( 18 \), the top is \( 18 + 8 = 26 \)? No, that's not. Wait, the triangle's base is \( 8 \), so the top side is \( 18 + 8 = 26 \), the left side is \( 15 \), the bottom side is \( 18 \), the right side is the hypotenuse \( 17 \), and the vertical side? Wait, no, the rectangle has height \( 15 \), so the left and right vertical sides (but the right vertical side is replaced by the triangle's vertical leg). Wait, I'm confused. Let's add all the outer sides:

• Left: \( 15 \)
• Top: \( 18 + 8 = 26 \)
• Hypotenuse: \( 17 \)
• Bottom: \( 18 \)
• Wait, no, that's only four sides. Wait, the rectangle has four sides, but the triangle is attached to one side, so we have to adjust. Wait, the original rectangle has sides \( 15, 18, 15, 18 \). Then we attach a triangle to the right \( 18 \) side? No, the figure shows the rectangle with length \( 18 \), height \( 15 \), and a triangle attached to the right end, with base \( 8 \) (horizontal), height \( 15 \) (vertical), hypotenuse \( 17 \). So the outer edges are:
• Left: \( 15 \)
• Bottom: \( 18 \)
• The vertical side from bottom right of rectangle up to the triangle's right angle: \( 15 \) (but that's internal)
• Then, the hypotenuse: \( 17 \)
• Then, the top horizontal side: \( 18 + 8 = 26 \)
• Then, the left vertical side: \( 15 \)

Wait, no, that's double-counting. Let's do it properly:
The perimeter is the sum of all the sides that form the boundary. So:

• Left vertical: \( 15 \)
• Top horizontal: \( 18 + 8 = 26 \)
• Hypotenuse: \( 17 \)
• Bottom horizontal: \( 18 \)
• Wait, that's four sides? No, the left vertical, top horizontal, hypotenuse, bottom horizontal, and the vertical side? No, the vertical side is \( 15 \), but it's between the bottom and top. Wait, I think I made a mistake. Let's calculate the perimeter by adding all the outer sides:
• Left: \( 15 \)
• Top: \( 18 + 8 = 26 \)
• Hypotenuse: \( 17 \)
• Bottom: \( 18 \)
• Wait, that's \( 15 + 26 + 17 + 18 = 76 \). Ah, that matches the first and third options. So perimeter is \( 76 \) feet.

Step 2: Calculate the Area

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

• Area of rectangle: \( \text{length} \times \text{height} = 18 \times 15 = 270 \) square feet.
• Area of triangle: \( \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 15 = 60 \) square feet.
• Total area: \( 270 + 60 = 330 \) square feet.

So the perimeter is \( 76 \) feet and the area is \( 330 \) square feet.

Answer:

), and a right triangle attached to the right, so the total length of the bottom is \( 18 \), the top is \( 18 + 8 = 26 \)? No, that's not. Wait, the triangle's base is \( 8 \), so the top side is \( 18 + 8 = 26 \), the left side is \( 15 \), the bottom side is \( 18 \), the right side is the hypotenuse \( 17 \), and the vertical side? Wait, no, the rectangle has height \( 15 \), so the left and right vertical sides (but the right vertical side is replaced by the triangle's vertical leg). Wait, I'm confused. Let's add all the outer sides:

• Left: \( 15 \)
• Top: \( 18 + 8 = 26 \)
• Hypotenuse: \( 17 \)
• Bottom: \( 18 \)
• Wait, no, that's only four sides. Wait, the rectangle has four sides, but the triangle is attached to one side, so we have to adjust. Wait, the original rectangle has sides \( 15, 18, 15, 18 \). Then we attach a triangle to the right \( 18 \) side? No, the figure shows the rectangle with length \( 18 \), height \( 15 \), and a triangle attached to the right end, with base \( 8 \) (horizontal), height \( 15 \) (vertical), hypotenuse \( 17 \). So the outer edges are:
• Left: \( 15 \)
• Bottom: \( 18 \)
• The vertical side from bottom right of rectangle up to the triangle's right angle: \( 15 \) (but that's internal)
• Then, the hypotenuse: \( 17 \)
• Then, the top horizontal side: \( 18 + 8 = 26 \)
• Then, the left vertical side: \( 15 \)

Wait, no, that's double-counting. Let's do it properly:
The perimeter is the sum of all the sides that form the boundary. So:

• Left vertical: \( 15 \)
• Top horizontal: \( 18 + 8 = 26 \)
• Hypotenuse: \( 17 \)
• Bottom horizontal: \( 18 \)
• Wait, that's four sides? No, the left vertical, top horizontal, hypotenuse, bottom horizontal, and the vertical side? No, the vertical side is \( 15 \), but it's between the bottom and top. Wait, I think I made a mistake. Let's calculate the perimeter by adding all the outer sides:
• Left: \( 15 \)
• Top: \( 18 + 8 = 26 \)
• Hypotenuse: \( 17 \)
• Bottom: \( 18 \)
• Wait, that's \( 15 + 26 + 17 + 18 = 76 \). Ah, that matches the first and third options. So perimeter is \( 76 \) feet.

Step 2: Calculate the Area

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

• Area of rectangle: \( \text{length} \times \text{height} = 18 \times 15 = 270 \) square feet.
• Area of triangle: \( \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 15 = 60 \) square feet.
• Total area: \( 270 + 60 = 330 \) square feet.

So the perimeter is \( 76 \) feet and the area is \( 330 \) square feet.