Question

the coordinate grid shows an equilateral triangle that fits inside a square.
a(-2,3), b(2,3), d(-2,-1), c(2,-1), e(0,√3), g(-1,0), f(1,0)
a. find the area of the square. show your work.
s = blank, so a = blank² = blank units²

Explanation:

Step1: Find the side length of the square

To find the side length \( s \) of the square, we can use the distance between two vertical or horizontal vertices. Let's take points \( A(-2, 3) \) and \( B(2, 3) \). The distance between them (which is the length of the horizontal side) is calculated by the difference in the \( x \)-coordinates (since the \( y \)-coordinates are the same). The formula for the distance between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) when \( y_1 = y_2 \) is \( |x_2 - x_1| \).

So, \( s = |2 - (-2)| = |2 + 2| = 4 \).

Step2: Calculate the area of the square

The formula for the area \( A \) of a square is \( A = s^2 \), where \( s \) is the side length. We found that \( s = 4 \), so we substitute \( s \) into the formula:

\( A = 4^2 = 16 \).

Answer:

\( s = \boldsymbol{4} \), so \( A = \boldsymbol{4}^2 = \boldsymbol{16} \) units\(^2\)