Triangles
What is the formula for the area of a triangle when given the base (b) and height (h)?
Area = 0.5 * base * height
What is the formula for the area of a trapezoid?
Area = 0.5 * (sum of bases) * height
Calculate the total area of a compound shape consisting of a square with side length 5 cm and a right triangle with base 4 cm and height 3 cm sharing a side.
31 square cm
A compound shape is made up of two rectangles and a triangle. If the dimensions of the rectangles are 4 units by 6 units and 3 units by 8 units, and the triangle has a base of 5 units and a height of 4 units, what is the total area of the compound shape?
58 square units
A triangle has a base of 6 cm and a height of 9 cm. Calculate its area.
27 square cm
A trapezoid has bases of 4 cm and 9 cm, and a height of 7 cm. Determine its area.
45.5 square cm
Calculate the area of a parallelogram with a base of 12 units and a height of 8 units.
96 square units
Why is it useful to be able to decompose a compound shape into simpler shapes to find its area?
Decomposing a compound shape into simpler shapes, such as rectangles and triangles, is useful because it allows you to calculate the area of the overall shape by adding the areas of the individual components. This makes it easier to find the total area, especially for more complex shapes.
How can you decompose a parallelogram into two congruent triangles to find its area?
By drawing a diagonal from one vertex to the opposite side.
Describe how you would compose a trapezoid into a rectangle and two right triangles to find its area.
By drawing a line parallel to the bases to create a rectangle and two right triangles.
Calculate the area of a parallelogram with a base of 6 units and a height of 9 units.
6 * 9 = 54 square units
Calculate the total area of a compound polygon composed of a triangle with base 3 units and height 6 units, and a rectangle with a length of 8 units and width of 4 units.
Area = (0.5 * 3 * 6) + (8 * 4) = 9 + 32 = 41 square units
For a right triangle with legs of lengths 5 cm and 12 cm, find the area.
30 square cm
If the area of a trapezoid is 75 square units, with bases of lengths 6 units and 9 units, what is its height?
10 units
If the base of a parallelogram is 12 cm and the height is 7 cm, what is its area?
Area = 12 * 7 = 84 square cm
A compound polygon is made up of a rectangle with dimensions 10m by 6m and a trapezoid with bases 8m and 5m and a height of 4m. Find the total area of the compound polygon.
Area = (10 * 6) + (0.5 * (8 + 5) * 4) = 60 + 26 = 86 square meters
A triangle has an area of 50 square units and a base of 5 units. What is its height?
Height=10 units
Discuss the similarities and differences between finding the area of a trapezoid and a triangle.
Both involve multiplying base by height, but trapezoid uses the sum of bases.
A parallelogram has a base of 15 inches and a height of 4 inches. What is its area?
Area = 15 * 4 = 60 square inches
A compound shape consists of a triangle with a base of 12 units and a height of 8 units, and a parallelogram with a base of 10 units and a height of 6 units. Find the total area of the compound polygon.
108 square units