Questions: Find a formula for the area of the figure shown to the right in terms of p. A= (Use integers or fractions for any numbers in the expression.)

$Find a formula for the area of the figure shown to the right in terms of p. A= (Use integers or fractions for any numbers in the expression.)$

Transcript text: Find a formula for the area of the figure shown to the right in terms of $p$. $A=$ $\square$ (Use integers or fractions for any numbers in the expression.)

Solution

Solution Steps

Step 1: Identify the type of triangle

The given triangle has two angles of 45° and one angle of 90°. This means it is a 45-45-90 right triangle, which is also an isosceles triangle.

Step 2: Determine the relationship between sides

In a 45-45-90 triangle, the two legs are congruent, both having length 'p' in this case. The hypotenuse is equal to leg * √2, so the hypotenuse here is p√2.

Step 3: Calculate the area

The area of a triangle is (1/2) * base * height. In this right triangle, the two legs serve as the base and height. So, the area A = (1/2) * p * p = (1/2)p².

Final Answer

$A = \frac{1}{2}p^2$

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