Question

The figure is made up of a square and a rectangle. Find the area of the shaded region.

Answer 1

36 meters squared.

Explanation:

A triangle's area can be found using the formula
`(1)/(2)`bh. We already know the height of the triangle as it's given. The height is 12m, same as the square's height. Now we must solve for the base of the triangle.

The larger object being a square is quite convenient. All four of its sides are equivalent in length. 12 m on all sides. We're looking for the base of the triangle which just so happens to share a base with the small rectangle. All we have to do is subtract the length of the square's base (12 m) from the overall total of both of the shape's bases.

18m = rectangle's base + 12 m

Thus:

18 - 12 = base

18 - 12 = 6

b = 6

We now have everything we need.

Area of a Triangle =
`(1)/(2)`bh

Height = 12

Base = 6

Plug in the numbers.

A =
`(1)/(2)`(6)(12)

A =
`(1)/(2)`(72)

A = 36 meters squared (36 m²)