Question

Amir is laying stone for his new patio. The diagram of the patio is shown. How many

Answer 1

Answer: 108ft^2

Step-by-step explanation:

First, at the top we have two triangle rectangles.

The area of a triangle rectangle is equal to the product of their cathetus divided by two.

We know that one common cathetus for both triangles is 6ft.

And both share the bottom line that is 14ft long, so half of that corresponds to each triangle.

14ft/2 = 7ft

Then each triangle has a cathetus of 6ft and one of 7ft.

Then the area of each triangle rectangle at the top is:

6ft*7ft/2 = 21ft^2

And we have two of them, so the area for now is:

A1 = 21ft^2 + 21ft^2 = 42ft^2.

Now let's look at the bottom part, we can divide this into two triangle rectangles and one rectangle.

First, bottom side is 8ft, then the difference between this side and the 14ft one is:

14ft - 8ft = 6ft

(We calculate this because we are making a rectangle, then the bottom side length must be equal than the top one).

Then we have a surpass of 6ft, which we will divide into both triangle rectangles (3ft for each, this is one of the cathetus).

And we can see that the cathetus shown of this triangle rectangle is 6ft (this is also the other side of our rectangle)

Then we have two triangles with cathetus 6ft and 3 ft, the area is:

A = 6ft*3ft/2 = 9ft^2

And we have two of them, then A2 = 18ft^2.

And the rectangle is 8ft by 6ft, the area is:

A3 = 8ft*6ft = 48ft^2

Then if we add all the areas that we found, we have:

A1 + A2 + A3 = 42ft^2 + 18ft^2 + 48ft^2 = 108ft^2