The composite figure has sides measuring 1 mi, 6 mi, 7 mi, 1 mi, 1 mi, and 3 mi. What is the area?
To find the area of the composite figure, we can break it down into smaller shapes.
The composite figure can be divided into a triangle with sides 1 mi, 6 mi, and 7 mi, a quadrilateral with sides 1 mi, 1 mi, 1 mi, and 3 mi, and a triangle with sides 3 mi, 6 mi, and 7 mi.
First, find the area of the triangle with sides 1 mi, 6 mi, and 7 mi using Heron's formula:
s = (1 + 6 + 7) / 2 = 7
Area = √[7(7-1)(7-6)(7-7)] = √[7(6)(1)(0)] = 0 square miles
Next, find the area of the quadrilateral with sides 1 mi, 1 mi, 1 mi, and 3 mi. Since the quadrilateral is a square, we can find the area by squaring any of the side lengths:
Area = (1)^2 = 1 square mile
Finally, find the area of the triangle with sides 3 mi, 6 mi, and 7 mi using Heron's formula:
s = (3 + 6 + 7) / 2 = 8
Area = √[8(8-3)(8-6)(8-7)] = √[8(5)(2)(1)] = √[80] ≈ 8.94 square miles
Add up the areas of the individual shapes to find the total area of the composite figure:
0 + 1 + 8.94 = 9.94 square miles
Therefore, the area of the given composite figure is approximately 9.94 square miles.