Question

Naomi used a rectangle, a square, and a right triangle to form the following figure. What is the area of the shaded region of the figure in square centimeters?

Answer 1

102cm²

Explanation:

Step 1 find the area of the whole rectangle

Area of a rectangle = width times length

The width of the rectangle is 20 cm and the length is 6cm

So the area = 20 * 6

20 * 6 = 120

Hence the area of the rectangle is 120 square centimeters.

Step 2 Find the area of the square and the triangle

Area of square = s²

where s = side length

The square has a side length of 3 so the area of the square = 3²

3² = 9

Hence, the area of the square is 9cm²

Now to find the area of the triangle

area of a triangle =
`(bh)/(2)` where b = base length and h = height

We are given the height (3 cm, this is given because the square is sharing it's side length with the height of the triangle.)

Now to find the base length

We can find it by subtracting the overall rectangle's width (20cm) by the bottom width (11 cm) and the bottom length of the square ( 3 cm )

so triangle's base length = 20 - 11 - 3

20 - 11 - 3 = 6

so the base length of the triangle is 6 cm

now we plug in the values of the height and the base length into the formula

`A=(6*3)/(2) \\6*3=18\\(18)/(2) =9`

Hence the area of the triangle is 9 cm²

Finally, to find the area of the shaded area, we subtract the area of the triangle and the area of the square from the area of the rectangle

so your answer = 120 - 9 - 9

120 - 9 - 9 = 102

Hence, the area of the shaded region is 102 square centimeters.