Question

What is the area of this shape?

Answer 1

We are going to have to take the area of multiple shapes and add them together.

Let's start with the left right triangle. We know that the base is 6 u (due to the triangle base being told as 3 u on the top of the figure), and the height is 8 u (due to the height being specified on the right triangle on the right side of the figure).

We also know that the area of a triangle is: $\frac{1}{2}bh$.

Let's solve for the right triangle:

$\frac{1}{2}(6)*(8)=24 units^{2}$

The two right triangles that are next are essentially one rectangle. And we know that the area of a rectangle is calculated by: $A=l*w$.

The w = 3 u as specified by the diagram, and the l = 8 units as also specified on the right side of the figure. Let's solve for the two triangles (or rectangle):

$A =(8)(3)=24 units^{2}$

Then we move on to the rectangle in the middle. The l of the rectangle is going to be 21 - 9 - 3 due to the total length of the figure being 21, and the length of the other pieces being specified in the diagram. So we just subtract those lengths from the total length to get the length of the rectangle. So the length is then 9 units. And we know the w = 8 units as specified in the diagram. So let's solve for the area:

$A=(9)(8)=72 units^{2}$

Then we only have one right triangle left. We know the base = 3 u, and the height = 8 u, so using the equation from earlier, let's solve for the area:

$\frac{1}{2}(3)(8)=12 units^{2}$

So in order to find the total area of the figure, let's add all of the areas of all of the pieces together:

$24 + 24 + 72 + 12 =132 units^{2}$

So we know that the total area of the figure is $132 units^{2}$.

Answer 2

I got 132 for the area of this shape