What is the area of this composite shape?

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in²

The image shows a polygon that looks like a rectangle with a triangle attached to the bottom right side of it. The polygon has 5 sides. The top side is 6 inches long. The left side is perpendicular to the top side and is 13 inches long. The right side is perpendicular to the top side also and is 7 inches long. A side at the bottom is perpendicular to the 7-inch side and is 3 inches long. It looks like it stops almost midway across the bottom. The last segment is slanted and connects the 3-inch segment to the left side. This slanted side is not labeled.

87 square inches  

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The area of the composite figure is equal to the area of a rectangle plus the area of a triangle

so

b

step-by-step explanation:

given

- 2 (3x + 12y - 5 - 17x - 16y + 4 )

simplify the parenthesis by collecting like terms

= - 2 (- 14x - 4y - 1) ← distribute the parenthesis by - 2

= 28x + 8y + 2 → b

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.