Find the area of each of the eight shapes in the composite figure.(In: The hexagon can broken into two trapezoids.)
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.