Question

Find the area of the following Shape. You must show all work toe receive credit

Answer 1

We are given a geometric figure and we are asked to determine its area. To do this we will divide the figure into three components, like this:

We have divided the figure into, figure 1 a triangle, figure 2 a triangle, and figure 3 a rectangle. To determine the area of figure 1 we will use the formula for the area of a triangle, which is:

$A_1=\frac{bh}{2}$

Where "b" is the base and "h" is the height. In this case, we have that the base of the first triangle measures 4 units, and its height measures 4 units. Replacing in the formula we get:

$A_1=\frac{(4)(4)}{2}$

Solving the operations we get:

$A_1=8$

This means that the area of the first triangle is 8 square units. Now we apply the same formula for the second triangle. In this case, the base is 2 units and its height is 2 units. Replacing in the formula we get:

$A_2=\frac{(2)(2)}{2}$

Solving the operations we get:

$A_2=2$

This means that the area of the second triangle is 2 square units. Now, to determine the area of the third figure, a rectangle we will use the following formula:

$A_3=bh$

Where "b" is the base and "h" is the height. In this case, we have that the base of the rectangle measures 1 unit and its height measures 2 units. Therefore, the area is:

$A_3=(1)(2)$

Solving the operations:

$A_3=2$

Therefore, the area of the rectangle is 2 square units. Now to determine the total area we will add up the areas of the three figures:

$A_T=A_1+A_2+A_3$

Replacing the values:

$A_T=8+2+2$

Solving the operations:

$A_T=12$

Therefore, the area of the figure is 12 square units.