Area of Parallelograms and Triangles
The area of a parallelogram is base × height. The height must be perpendicular to the base, not the slanted side. The area of a triangle is exactly half of this: ½ × base × height.
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Height of a Parallelogram
- The height h is perpendicular to the base b.
- The height goes from the base to the opposite side, even if it is outside.
Area of a Parallelogram
- The area of a parallelogram is found using base × height.
- This is written as
Height of a Triangle
- The height h is perpendicular to the base b.
- The height goes from the base to the opposite vertex.
Area of a Triangle
- The area of a triangle is half the area of a parallelogram.
- The formula is .
Practice Questions
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What is the formula for the area of a parallelogram?
Correct! 🎉 +10 pointsNot quite right
The area of a parallelogram is calculated using the formula: base times height. The height is always perpendicular to the base, extending from the base to the opposite side.
What does the height of a triangle always do?
Correct! 🎉 +10 pointsNot quite right
The height of a triangle is always perpendicular to the base and extends from the base to the opposite vertex.
If the base of a parallelogram is and the height is , what is its area?
Correct! 🎉 +20 pointsNot quite right
The area of a parallelogram is calculated by multiplying the base by the height: .
What is the area of this parallelogram?
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The area of a parallelogram is calculated by multiplying the base by the height: .
What is the area of this triangle?
Correct! 🎉 +20 pointsNot quite right
The area of a triangle is calculated using the formula × base × height. Multiply by and then halve it to get .
What is the area of the parallelogram shown in the image?
Correct! 🎉 +30 pointsNot quite right
The side is not the height because it is not perpendicular to the base. Without information about the height, the area cannot be determined from the image alone.
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The area of a parallelogram is base times height, written as Area = b × h. Here, the base (b) is any one of the parallelogram's sides. The height (h) is the perpendicular distance from that base to the opposite side, not the slanted side.
The area of a triangle is half the base times the height. The formula is Area = ½ × b × h. The base (b) is any one of the three sides. The height (h) is the perpendicular distance from that base to the opposite vertex, not a slanted side.
When you double a triangle, you create a parallelogram with the same base and height. You do this by copying the triangle, rotating the copy and joining the two together. Since the parallelogram's area is base times height, the triangle takes exactly half. So Area = ½ × base × height for any triangle.
A parallelogram can always be turned into a rectangle with the same base and the same perpendicular height. Both shapes therefore cover exactly the same amount of space. So they share the same area formula: Area = base × height.
Yes. A parallelogram that leans far over, or a triangle with an obtuse angle, has its perpendicular height outside the shape. In these cases, you extend the base in a straight line until the perpendicular meets it. Then you measure the height from the extended base.