Answer:
The area of the shaded region is:
Step-by-step explanation:
First, we're gonna find the area of the whole rectangle and next we can subtract the area of the triangles in the corners, we use the next formula:
- Area of a rectangle = width * heigth
And we replace the measurements in the picture (32 ft and 16 ft):
- Area of a rectangle = 16 ft * 32 ft
- Area of a rectangle = 512 ft^2
Now, we must calculate the area of a triangle, this can be made by this formula:
- Area of a triangle = (base * height) / 2
We can replace the values we have in the picture (4 ft and 6 ft), then:
- Area of a triangle = (4 ft * 6 ft) / 2
- Area of a triangle = (24 ft^2)/ 2
- Area of a triangle = 12 ft^2
As you can see in the picture, we have to subtract two triangles with the same measurements, by this reason, we multiply the area of the triangle by two and we'll obtain the area we must subtract:
- Area to subtract = (12 ft^2) * 2
- Area to subtract = 24 ft^2
At last, we take the area of the whole rectangle and subtract the area of the triangles:
- Area of the shaded region = 512 ft^2 - 24 ft^2
- Area of the shaded region = 488 ft^2
The area of the shaded region is 488 ft^2.
