Sam created the figure below using a rectangle and two congruent triangles. The side lengths of the rectangle and the base and height of the triangles are shown
What is the area of the shaded region in square inches?

a.112.5in
b.105in
c.135in
d.120in

b. 105 in

Step-by-step explanation:

Area of a triangle = ½ bh [base × height].

Area of a rectangle = lw [length × width].

The shaded region is taken up by the two triangles which means that you subtract the area of the rectangle from the two triangles.

Assuming that the two triangles are congruent [same shape and size], the area of the two triangles are really just the base times the height because ½bh + ½bh = bh.

So 3 × 5 = 15 in.

The area of the rectangle shown is its length times it's width which is 15 × 8 = 120in.

Now just subtract the area of the rectangle from the area of the triangles that are taking up the area:

Therefore,

Area of the rectangle – Area of the triangles = shaded area

120in – 15in = 105in = shaded area.