Question

find a formula for the area of the figure shown to the right in terms of y

a=box (use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Identify the triangle type

The triangle is a right - isosceles triangle (since two angles are \(45^{\circ}\) and one is \(90^{\circ}\)), so the two legs (the sides forming the right angle) are equal, both equal to \(y\).

Step2: Recall the area formula for a triangle

The area formula for a triangle is \(A=\frac{1}{2}\times base\times height\). For a right - triangle, the base and height are the two legs. Here, base \( = y\) and height \( = y\).

Step3: Substitute the values into the formula

Substitute base \(=y\) and height \(=y\) into the area formula \(A = \frac{1}{2}\times base\times height\). We get \(A=\frac{1}{2}\times y\times y\).

Step4: Simplify the expression

Simplify \(\frac{1}{2}\times y\times y\) using the rule of exponents \(a\times a=a^{2}\). So \(A = \frac{1}{2}y^{2}\).

Answer:

\(\frac{1}{2}y^{2}\)