Answer:
A = 139.5 cm^2
Step-by-step explanation:
Ok, let's break it down into pieces. First let's find the area of the main rectangle. We know that the area of a rectangle is as follows:
A = L x W
A = 9 x 12
A = 108 cm^2
Now we need to find the area of the two triangles. There are two ways to approach this. If you can visualize that you can flip the first triangle and slide it against the second, it becomes a rectangle. Then you can simply use the same formula as before with modified numbers.
L = 7 (height of the triangle
W = 4.5 (base of the triangle (half of 9))
A (both triangles) = 7 x 4.5
A (both triangles) = 31.5 cm^2
If you can't quite figure out how to visualize that, you can simply treat them as two independent right triangles. The formula for the area of a right triangle is as follows:
A = (1/2)b x h
b = 4.5
h = 7
A (first triangle) = (1/2)4.5 x 7
A (first triangle) = 15.75 cm^2
The area of the second triangle is identical
A (second triangle) = 15.75 cm^2
The area of the two triangles added together is
A (both triangles) = A (first triangle) + A (second triangle)
A (both triangles) = 31.5 cm^2
As you can see we got the same answer both ways. Now we just have to add the area of the two triangles to the area of the rectangle
A = 108 + 31.5
A = 139.5 cm^2
