Answer:
68 inches squared
Step-by-step explanation:
First, let's find the area of the squares at the top and bottom. Area for a square is:
L * W = A
Plug in the values...
3 * 3 = 9
Therefore, the area of the two squares combined is 18 inches (since 9 + 9 = 18). Now, the hexagon in the middle, which is the hardest part. We will have to separate it into 4 triangles and a rectangle, for simplification. We need to find the base widths of the triangles, which are:
7 (total width) - 3 (middle width) / 2 (because there are two sides)
So it is:
(7 - 3)/2
4/2 = 2
So, the base of the triangle is two inches. We also know that the height of the triangle is five inches. The formula for the area of a triangle is:
(B * H)/2 = A
Fill it in...
(2 * 5)/2
10/2 = 5 inches
So, the area of each triangle is 5 inches. Since there are four triangles, we need to do:
5 * 4 = 20 inches
That means that all of the triangles combined is 20 inches. Lastly, we need the middle part of our hexagon. It is 10 inches tall, and three inches wide. So...
L * W = A
10 * 3 = 30
So, that means that the area of the hexagon is:
30 + 20 = 50
Plus, the two squares from the beginning:
50 + 18 = 68 inches squared
Therefore, the area of the figure is 68 inches. Hope this helps you!
