Area of a Complex Figure
What is the area of this figure?
When we find the area of figures with right angles by dividing it into smaller rectangles and calculate the area, we are doing the same thing with complex figures, except instead of only rectangles, we also divide into triangles.
The smartest and easiest way to divide this figure is separating the obvious looking rectangle and triangle. Then labeling the dimension of the dashed line.
Then we add the area of the rectangle and the area of the triangle together to find the total area of this figure.
Area of rectangle: 7 x 10 = 70
Area of triangle: 6 x 9 / 2 = 27
Total area: 97
What is the area of this figure?
We start by dividing this figure into polygons. And the left over spaces should look like polygons too. If not, keep dividing until you see polygons for every region.
You can divide this figure into many ways, but try and find the easiest and most obvious.
Area of bigger rectangle: 10 x 6 = 60
Area of smaller rectangle: 3 x 4 = 12
Area of triangle: 7 x 4 / 2 = 14
Total area: 86
A square sheet of paper with an area 81 inches has a corner cut off, forming a pentagon as shown above.
What is the perimeter?
A sheet with an area of 81 inches could only mean that the measurements on each side were 9 inches. We create the cut off corner into a triangle and label the sides.
Then we count the sides.
9 + 9 + 6 + 5 + 3 + 4 = 34 inches
Answer: 34 inches
What is the area of the pentagon above?
We knew before it was 81 inches in area, but since a corner was cut off, we have to subtract from the original area of 81 inches. We first find the area of the triangle.
3 x 4 / 2 = 6
So we subtract 6 from 81 and get 75 inches.
Answer: 75 inches