Question

Given the figure find the total area of the shaded region

Answer 1

Step-by-step explanation:

Consider the following figure:

To find the total area of the shaded region we must first find the area of the triangle and the area of the rectangle that contains this triangle.

Let us denote by A1 the area of the rectangle that contains the triangle and by A2 the area of the triangle.

Then, according to the figure, we have that:

`A1=\text{ base x height =9 x 6 = 54}`

and

`A2\text{ =}\frac{base\text{ x height }}{2}=\frac{6\text{ x 4}}{2}=6\text{ x2 = 12}`

Now, area A of the shaded region is given by the following equation:

`A\text{ = A1 - A2 }`

applying the data that we obtained in the previous calculations, we get:

`A\text{ = A1 - A2 =54 - 12 = 42}`

we can conclude that the correct answer is:

Answer:
`42\text{ }`