Answer:
The area of the shaded region of the figure in the exercise is:
Step-by-step explanation:
To obtain the area of irregular shapes, you can divide that shape in figure you know and you can obtain the area, first, we're gonna calculate the area of the right side and the left side with the formula below:
- Area of a rectangle = base * height.
- Area of right rectangle = 1.6 in * 5.2 in
- Area of right rectangle = 8.32 [tex]in^{2}[/tex]
How the left rectangle and the right rectangle have the same measurements, we can say:
- Area of left rectangle = 8.32 [tex]in^{2}[/tex]
You can see in the center there is a rectangle too, but you need just a half formed by a triangle, you can use two form for this: calculating the area of the triangle or calculating the area of the whole rectangle and next to divide in 2, we're gonna use the first:
- Area of triangle = (base * height) / 2
In the exercise, the base of the shaded triangle is 2.7 inches, and the height you must add the measurements in the right side:
- Height of the triangle = 1.6 in + 5.2 in + 1.6 in
- Height of the triangle = 8.4 in
Now we replace in the formula:
- Area of triangle = (2.7 in * 8.4 in) / 2
- Area of triangle = 22.68 [tex]in^{2}[/tex] / 2
- Area of triangle = 11.34 [tex]in^{2}[/tex]
By last, you must add all the calculated areas from the shaded regions:
- Area of the shaded region = 8.32 [tex]in^{2}[/tex] + 8.32 [tex]in^{2}[/tex] + 11.34 [tex]in^{2}[/tex]
- Area of the shaded region = 27.98 [tex]in^{2}[/tex]
