Question

calculate the area of each right triangle below. note that the figures are not drawn to scale.
1.
2.
3.
4.
5.

Explanation:

Step1: Recall area formula for right triangles

The area of a right triangle is $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$, where base and height are the two perpendicular sides (legs) of the triangle.

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For Triangle 1:

Step2: Identify base and height

Base = $31.2\ \text{cm}$, Height = $9.1\ \text{cm}$

Step3: Calculate area

$\text{Area} = \frac{1}{2} \times 31.2 \times 9.1 = 141.96\ \text{cm}^2$

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For Triangle 2:

Step4: Identify base and height

Base = $5\ \text{km}$, Height = $3\frac{3}{4} = 3.75\ \text{km}$

Step5: Calculate area

$\text{Area} = \frac{1}{2} \times 5 \times 3.75 = 9.375\ \text{km}^2$

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For Triangle 3:

Step6: Identify base and height

Base = $2.4\ \text{in}$, Height = $3.2\ \text{in}$

Step7: Calculate area

$\text{Area} = \frac{1}{2} \times 2.4 \times 3.2 = 3.84\ \text{in}^2$

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For Triangle 4:

Step8: Identify base and height

Base = $60\ \text{mm}$, Height = $11\ \text{mm}$

Step9: Calculate area

$\text{Area} = \frac{1}{2} \times 60 \times 11 = 330\ \text{mm}^2$

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For Triangle 5:

Step10: Identify base and height

Base = $10\ \text{ft}$, Height = $13\frac{1}{3} = \frac{40}{3}\ \text{ft}$

Step11: Calculate area

$\text{Area} = \frac{1}{2} \times 10 \times \frac{40}{3} = \frac{200}{3} \approx 66.67\ \text{ft}^2$

Answer:

1. $141.96\ \text{cm}^2$
2. $9.375\ \text{km}^2$
3. $3.84\ \text{in}^2$
4. $330\ \text{mm}^2$
5. $\frac{200}{3}\ \text{ft}^2$ (or $66.67\ \text{ft}^2$)