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Questions and Answers
What is the area of a parallelogram with a base of 20 cm and a height of 12 cm?
What is the area of a parallelogram with a base of 20 cm and a height of 12 cm?
Given a triangle with a base of 7 m and a height of 4 m, what is its area?
Given a triangle with a base of 7 m and a height of 4 m, what is its area?
For a parallelogram with an area of 112 unit² and a base of 10 units, what is the height?
For a parallelogram with an area of 112 unit² and a base of 10 units, what is the height?
How do you find the height of a triangle if the area is 13.5 yd² and the base is 4.5 yd?
How do you find the height of a triangle if the area is 13.5 yd² and the base is 4.5 yd?
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What is the area of a triangle with a base of 2 ft and a height of 3 ft?
What is the area of a triangle with a base of 2 ft and a height of 3 ft?
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Study Notes
Lesson Objectives
- Find the area of parallelograms and triangles.
Parallelograms
- Area formula: Area = base × height (A = b × h)
- Height is the perpendicular distance from the base to the opposite side.
- Examples provided with calculations:
- A parallelogram with base 20 cm and height 12 cm has an area of 240 cm².
- Another with base 4.7 inches and height 5.7 inches has an area of 26.79 in².
- A final example with base 5.8 m and height 3.5 m has an area of 20.3 m².
Finding the Height of a Parallelogram
- If the area and base are known, the height can be calculated: height = area ÷ base (h = A ÷ b)
- Examples:
- A parallelogram with area 112 square units and base 10 units has a height of 11.2 units.
- Another with area 0.12 square units and base 0.5 units has a height of 0.24 units.
- A final example with area 216 square units and base 13 units has a height of 16.62 units.
Triangles
- Area formula: Area = ½ × base × height (A = ½ × b × h)
Examples of Triangle Area Calculations
- A triangle with base 7 and height 4 has an area of 14.
- A triangle with base 4.5 and height 6 has an area of 13.5.
- A triangle with base 2 and height 3 has an area of 3.
Urban Design Problem (Problem 17)
- A parking lot problem involving finding the area of a paved surface that combines the areas of parking spaces (parallelograms), a rectangular driving region, and two triangular flowerbeds.
- Methods include adding the areas of the individual shapes and subtracting the areas of the flowerbeds to find an overall area. Methods for finding the area include using the parallelogram and triangle area formulas for individual parts and then combining these to find the total area.
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Description
Test your understanding of calculating the area of parallelograms and triangles with this quiz. You'll apply formulas and examples to find areas and heights, solidifying your concepts in geometry. Challenge yourself to master these essential skills!
