Question

What is the surface area of this figure?

Answer 1

Answer:

72 sq. mi

Step-by-step explanation:

Breaking this down, we have 2 right triangles with sides of 3, 4, and 5 miles, and 3 rectangles with dimensions 3 x 5, 4 x 5, and 5 x 5 miles. Remember that the area of a triangle is 1/2 x b x h , where b and h are the triangle's base and height. The base and height of the triangles at the bases of the figure are 3 and 4, so each triangle has an area of 1/2 x 3 x 4 = 1/2 x 12 = 6 sq. mi, or 6 + 6 = 12 sq. mi together.

Onto the rectangles, we can find their area by multiplying their length by their width. Since the width of these rectangles is the same for all three - 5 mi - we can make our lives a little easier and just "glue" the lengths together, giving us a longer rectangle with a length of 3 + 4 + 5 = 12 mi. Multiplying the two, we find the area of the rectangles to be 5 x 12 = 60 sq. mi.

Adding this area to the triangle's area gives us a total area of 12 + 60 = 72 sq. mi.

Answer 2

Answer:

72 mi^2.

Step-by-step explanation:

This consists of 2 congruent triangles and 3 rectangles.

Te area of a triangle = 1/2 * base * height and the area of a rectangle = length * width.  So:

Surface area = (2 * 1/2 * 3 * 4) + 5 * 5 + 5 * 4 + 5 * 3

= 12 + 25 + 20 + 15

= 72 mi^2.