How to find the area of a 45/45/90 right isosceles triangle - High School Math

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Question

The base of a right isosceles triangle is 8 inches. The hypotenuse is not the base. What is the area of the triangle in inches?

Answer

To find the area of a triangle, multiply the base by the height, then divide by 2. Since the short legs of an isosceles triangle are the same length, we need to know only one to know the other. Since, a short side serves as the base of the triangle, the other short side tells us the height.

$(8\cdot 8)/2=32$

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Question

An isosceles right triangle has a hypotenuse of $h=18\sqrt{2} in$ . Find its area.

Answer

In order to calculate the triangle's area, we need to find the lengths of its legs. An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as $45^{\circ}-45^{\circ}-90^{\circ}$ triangles and their side lengths follow a specific pattern that states that one can calculate the length of the legs of an isoceles triangle by dividing the length of the hypotenuse by the square root of 2.

$x=\frac{h}{\sqrt{2}}$

$x=\frac{18\sqrt{2}in}{\sqrt{2}}$

Now we can calculate the area using the formula

$A=\frac{1}{2}bh$

$A=\frac{1}{2}18in18in$

$A=162in^{2}$

Now, convert to feet.

$\rightarrow \frac{162 in^{2}}{1}\frac{1ft}{12in}\frac{1ft}{12in}=1.125ft^{2}$

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