To find the area of each shape in the composite figure, we first need to identify and calculate the areas of the individual shapes:
1. Rectangle: Since the length is 3 units and the width is 8 units, the area of the rectangle is:
Area = length x width = 3 units x 8 units = 24 square units
2. Triangle: The base of the triangle is 4 units and the height is 3 units, so the area of the triangle is:
Area = 1/2 x base x height = 1/2 x 4 units x 3 units = 6 square units
3. Hexagon (broken into two trapezoids):
Each trapezoid has a height of 3 units, bases of 5 units and 8 units. To find the area of each trapezoid, we can use the formula for the area of a trapezoid:
Area = 1/2 x (base1 + base2) x height
Area of the first trapezoid = 1/2 x (5 units + 8 units) x 3 units = 1/2 x 13 units x 3 units = 19.5 square units
Area of the second trapezoid = 1/2 x (5 units + 8 units) x 3 units = 1/2 x 13 units x 3 units = 19.5 square units
4. Parallelogram: The base of the parallelogram is 3 units and the height is 5 units, so the area is:
Area = base x height = 3 units x 5 units = 15 square units
5. Trapezoid: The bases of the trapezoid are 3 units and 5 units, and the height is 2 units. Using the formula for the area of a trapezoid:
Area = 1/2 x (base1 + base2) x height = 1/2 x (3 units + 5 units) x 2 units = 1/2 x 8 units x 2 units = 8 square units
Adding up the areas of all the shapes:
Total Area = Rectangle + Triangle + 2(Trapezoid) + Parallelogram + 2(Hexagon)
Total Area = 24 sq units + 6 sq units + 2(19.5 sq units) + 15 sq units + 2(8 sq units)
Total Area = 24 sq units + 6 sq units + 39 sq units + 15 sq units + 16 sq units
Total Area = 100 square units
Therefore, the total area of the composite figure is 100 square units.
Find the area of each of the eight shapes in the composite figure.(In: The hexagon can broken into two trapezoids.)
1 answer