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Area of Parallelograms and Triangles

Geometry and Measures Area of Parallelograms and Triangles

🎬 Video Tutorial

(0:01) Height of Parallelogram: The height ($h$) is always perpendicular to the base and may lie inside or outside the parallelogram.
(0:40) Area of a Parallelogram: The formula is $A = b \times h$, where $b$ is the base and $h$ is the perpendicular height.
(1:15) Height of Triangle: Like in a parallelogram, the triangle’s height is perpendicular to the base and can lie inside or outside, extending from the base to the opposite vertex.
(1:52) Area of a Triangle: The area of a triangle is $A = \frac{1}{2} \times b \times h$, derived by visualising the triangle as half of a rectangle or parallelogram with the same base and height.

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📂 Revision Cards

Height of a parallelogram illustrated with a perpendicular height h from base b to the opposite side. — 1) Height of a Parallelogram

Diagram showing the formula for the area of a parallelogram, A = b?h, with labelled base (b) and height (h) on two parallelograms. — 2) Area of a Parallelogram

Height of a triangle, with height h perpendicular to base b and extending from b to the opposite vertex, illustrated with two triangle diagrams. — 3) Height Triangle

Formula for the area of a triangle with base and height labelled, showing two triangles with base (b) and height (h). — 4) Area Triangle

🍪 Quiz

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Area of Parallelograms and Triangles

1 / 6

Q: What is the formula for the area of a parallelogram?

2 × Base × Height

Base × Height

Base ÷ Height

Base + Height

Feedback: Not quite! 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.

Feedback: Well done! 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.

2 / 6

Q: What does the height of a triangle always do?

It is parallel to the base.

It connects two opposite vertices.

It is perpendicular to the base.

It extends beyond the triangle.

Feedback: Not quite! The height of a triangle is always perpendicular to the base and extends from the base to the opposite vertex.

Feedback: Well done! The height of a triangle is always perpendicular to the base and extends from the base to the opposite vertex.

3 / 6

Q: If the base of a parallelogram is 6 cm and the height is 4 cm, what is its area?

$Yellow parallelogram with a base of 6 cm and a perpendicular height of 4 cm.$

$36 \, \text{cm}^2$

$10 \, \text{cm}^2$

$6 \, \text{cm}^2$

$24 \, \text{cm}^2$

Feedback: Not quite! The area of a parallelogram is calculated by multiplying the base by the height: 6 cm × 4 cm = 24 cm².

Feedback: Well done! The area of a parallelogram is calculated by multiplying the base by the height: 6 cm × 4 cm = 24 cm².

4 / 6

Q: What is the area of this parallelogram?

$Red parallelogram with a base of 8 cm and a perpendicular height of 5 cm.$

$30 \, \text{cm}^2$

$20 \, \text{cm}^2$

$40 \, \text{cm}^2$

$25 \, \text{cm}^2$

Feedback: Not quite! TThe area of a parallelogram is calculated by multiplying the base by the height: 5 cm × 8 cm = 40 cm².

Feedback: Well done! The area of a parallelogram is calculated by multiplying the base by the height: 5 cm × 8 cm = 40 cm².

5 / 6

Q: What is the area of this triangle?

$Green triangle with a base of 10 cm and a perpendicular height of 5 cm.$

$15 \, \text{cm}^2$

$25 \, \text{cm}^2$

$50 \, \text{cm}^2$

$5 \, \text{cm}^2$

Feedback: Not quite! The area of a triangle is calculated using the formula $\frac{1}{2}$ × base × height. Ensure you multiply 10 cm (base) by 5 cm (height) and then halve it to get 25 cm².

Feedback: Well done! The area of a triangle is calculated using the formula $\frac{1}{2}$ × base × height. Ensure you multiply 10 cm (base) by 5 cm (height) and then halve it to get 25 cm².

6 / 6

Q: What is the area of the parallelogram shown in the image?

$A blue parallelogram with a base measuring 6 cm and a slanted side measuring 14 cm.$

$40 \, \text{cm}^2$

Cannot be determined from the image alone.

$30 \, \text{cm}^2$

$50 \, \text{cm}^2$

Feedback: Not quite! In this case, the 14 cm side is not the height because it is not perpendicular to the base. Therefore, without the information about the height, the area cannot be determined from the image alone.

Feedback: Well done! In this case, the 14 cm side is not the height because it is not perpendicular to the base. Therefore, without the information about the height, the area cannot be determined from the image alone.

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