Question

Describe a method you can use to find the area of the following shape. Provide specific details in your answer, including coordinates and descriptions of shapes used. Then, find the actual area of the figure. (8 points)

Answer 1

There are a number of ways this can be done. One that is fairly simple is as follows.

Triangle ABC has base AC = 9 and height B to AC of 3 (found by counting squares). Thus its area is ∆ABC = (1/2)·9·3 = 13.5 square units.

Triangle ACF has base AC = 9 and height F to AC of 3, so will have the same area as triangle ABC, 13.5 square units.

Trapezoid CDEF has base CD of 6, base EF of 4 and height EF to CD of 6 (found by counting squares). Thus its area is CDEF = (1/2)(6 + 4)(6) = 30.

The total area of the entire figure is then

... ∆ABC + ∆ACF + CDEF = 13.5 + 13.5 + 30 = 57 square units.