Question

6 formula 0.5 points
given the following composite figure, d = 8.7 cm and w = 15.0 cm.
what is the perimeter of the figure?
image of a composite figure with two semicircles (forming a circle) and a rectangle, d is the diameter, w is the length
use 3.14 for pi, and round your answer to the nearest hundredth. do not include \cm\ with your response.
answer

7 formula 0.5 points
in the following figure, ab = 7 cm, bc = 3 cm, cd = 1 cm, de = 2 cm, ef = 3 cm, and fg = 1 cm.
what is the perimeter of the figure?
image with a to b horizontal, a right angle, then other sides
a b

Explanation:

Question 6

Step1: Identify the components of the perimeter

The composite figure has two semicircles (which make a full circle) and two straight sides of length \( w \). The diameter of the circle is \( d = 8.7 \) cm, so the circumference of the circle is \( C=\pi d \). The two straight sides each have length \( w = 15.0 \) cm, so their total length is \( 2w \).

Step2: Calculate the circumference of the circle

Using \( \pi = 3.14 \) and \( d = 8.7 \) cm, the circumference \( C = 3.14\times8.7 \).
\( 3.14\times8.7 = 27.318 \)

Step3: Calculate the total length of the straight sides

The two straight sides have length \( 2\times15.0 = 30.0 \)

Step4: Calculate the perimeter

The perimeter \( P \) is the sum of the circumference of the circle and the total length of the straight sides. So \( P=27.318 + 30.0 \)
\( P = 57.318 \), rounded to the nearest hundredth is \( 57.32 \)

Step1: Analyze the horizontal sides

The top horizontal side \( AB = 7 \) cm. The bottom horizontal side will also be \( 7 \) cm (due to the nature of the right - angled figure, the horizontal lengths are equal). So the total length of horizontal sides is \( 7 + 7=14 \) cm.

Step2: Analyze the vertical sides

The right - hand vertical sides: \( BC = 3 \) cm, \( DE = 2 \) cm, \( FG = 1 \) cm. The sum of these is \( 3 + 2+1 = 6 \) cm. The left - hand vertical side will be equal to the sum of the right - hand vertical sides (because it's a right - angled figure, the vertical lengths are equal). So the total length of vertical sides is \( 6+6 = 12 \) cm.

Step3: Calculate the perimeter

The perimeter \( P \) is the sum of the total horizontal and total vertical lengths. So \( P=14 + 12=26 \)

Answer:

\( 57.32 \)

Question 7

(Assuming the figure is a rectangle - like shape with some indentations, and we need to consider the horizontal and vertical sides. Since it's a right - angled figure (with the right angle at the bottom left, probably), the perimeter can be calculated by considering the top and bottom horizontal lengths and the left and right vertical lengths. The top length \( AB = 7 \) cm, so the bottom length (after considering the indentations) should also be \( 7 \) cm (because in a rectangle - like figure with vertical sides, the horizontal lengths are equal). For the vertical sides: the right side is \( BC + DE+ FG=3 + 2+1 = 6 \) cm, and the left side should be equal to the right side (since it's a right - angled figure, the vertical lengths are equal).)