Area of composite figures quick check
1. Find the area of the composite figure below:
______
/ \
/ \
| |
| |
| |
\ /
\_________/
To find the area of this composite figure, we will divide it into two simpler shapes: a rectangle and a triangle.
Rectangle:
- Length = 6 units
- Width = 4 units
Area of rectangle = length x width = 6 units x 4 units = 24 square units
Triangle:
- Base = 4 units
- Height = 3 units
Area of triangle = (1/2) x base x height = (1/2) x 4 units x 3 units = 6 square units
Total area of the composite figure = area of rectangle + area of triangle = 24 square units + 6 square units = 30 square units
Therefore, the area of the composite figure is 30 square units.
2. Find the area of the composite figure below:
__________________________
| |
| |
| 8 |
| |
|__________________________|
| |
| /\ |
| / \ |
| / \ |
| / \ |
| /________\ |
| 6 |
|__________________________|
To find the area of this composite figure, we will divide it into three simpler shapes: a rectangle, a trapezoid, and a triangle.
Rectangle:
- Length = 8 units
- Width = 3 units
Area of rectangle = length x width = 8 units x 3 units = 24 square units
Trapezoid:
- Bases = 12 units (8 units + 4 units)
- Height = 4 units
Area of trapezoid = (1/2) x (sum of bases) x height = (1/2) x 12 units x 4 units = 24 square units
Triangle:
- Base = 3 units
- Height = 6 units
Area of triangle = (1/2) x base x height = (1/2) x 3 units x 6 units = 9 square units
Total area of the composite figure = area of rectangle + area of trapezoid + area of triangle = 24 square units + 24 square units + 9 square units = 57 square units
Therefore, the area of the composite figure is 57 square units.