Question

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find the area of the triangle. round your answer to the nearest tenth. (choose the answer closest to yours since we are using radicals in calculators) a) 25.7 b) 22.9 c) 20 d) 30.5

Explanation:

Step1: Identify triangle sides

This is a right isosceles triangle, so both legs are equal: let each leg length be $x$. The hypotenuse is $9$.

Step2: Use Pythagorean theorem

$$x^2 + x^2 = 9^2$$
$$2x^2 = 81$$
$$x^2 = \frac{81}{2}$$
$$x = \sqrt{\frac{81}{2}} = \frac{9}{\sqrt{2}}$$

Step3: Calculate triangle area

Area formula for right triangle: $\text{Area} = \frac{1}{2} \times \text{leg}_1 \times \text{leg}_2$
$$\text{Area} = \frac{1}{2} \times \frac{9}{\sqrt{2}} \times \frac{9}{\sqrt{2}}$$
$$\text{Area} = \frac{1}{2} \times \frac{81}{2} = \frac{81}{4} = 20.25$$

Step4: Round to nearest tenth

$20.25 \approx 20.3$, which is closest to 20.

Answer:

C) 20