Area of Right Triangle Worksheets - Free Printable

Problem Overview:

The task involves calculating the area of right triangles by using the formula for the area of a triangle, which is:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

For each right triangle, the base and height are given as the two perpendicular sides. The solution will involve identifying the base and height for each triangle and applying the formula.

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Step-by-Step Solution:

#### Example:
- Given: A right triangle with legs of 5 cm and 4 cm.
- Formula:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
- Substitute values:
\[
\text{Area} = \frac{1}{2} \times 5 \, \text{cm} \times 4 \, \text{cm} = \frac{1}{2} \times 20 \, \text{cm}^2 = 10 \, \text{cm}^2
\]
- Answer: The area of the triangle is \( 10 \, \text{cm}^2 \).

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#### Question 1:
- Given: A right triangle with legs of 3 cm and 8 cm.
- Formula:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
- Substitute values:
\[
\text{Area} = \frac{1}{2} \times 3 \, \text{cm} \times 8 \, \text{cm} = \frac{1}{2} \times 24 \, \text{cm}^2 = 12 \, \text{cm}^2
\]
- Answer: The area of the triangle is \( 12 \, \text{cm}^2 \).

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#### Question 2:
- Given: A right triangle with legs of 6 cm and 9 cm.
- Formula:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
- Substitute values:
\[
\text{Area} = \frac{1}{2} \times 6 \, \text{cm} \times 9 \, \text{cm} = \frac{1}{2} \times 54 \, \text{cm}^2 = 27 \, \text{cm}^2
\]
- Answer: The area of the triangle is \( 27 \, \text{cm}^2 \).

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#### Question 3:
- Given: A right triangle with legs of 10 cm and 10 cm.
- Formula:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
- Substitute values:
\[
\text{Area} = \frac{1}{2} \times 10 \, \text{cm} \times 10 \, \text{cm} = \frac{1}{2} \times 100 \, \text{cm}^2 = 50 \, \text{cm}^2
\]
- Answer: The area of the triangle is \( 50 \, \text{cm}^2 \).

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#### Question 4:
- Given: A right triangle with legs of 1 m and 1 m.
- Formula:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
- Substitute values:
\[
\text{Area} = \frac{1}{2} \times 1 \, \text{m} \times 1 \, \text{m} = \frac{1}{2} \times 1 \, \text{m}^2 = 0.5 \, \text{m}^2
\]
- Answer: The area of the triangle is \( 0.5 \, \text{m}^2 \).

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#### Question 5:
- Given: A right triangle with legs of 22 cm and 10 cm.
- Formula:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
- Substitute values:
\[
\text{Area} = \frac{1}{2} \times 22 \, \text{cm} \times 10 \, \text{cm} = \frac{1}{2} \times 220 \, \text{cm}^2 = 110 \, \text{cm}^2
\]
- Answer: The area of the triangle is \( 110 \, \text{cm}^2 \).

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Final Answers:

\[
\boxed{12 \, \text{cm}^2, 27 \, \text{cm}^2, 50 \, \text{cm}^2, 0.5 \, \text{m}^2, 110 \, \text{cm}^2}
\]