Question

solve.
a diagonal divides a square cake that is 8 in. on a side.
what is the area on either side of the diagonal?
the math club has a flag in the shape of a right
triangle. it has a height of 12 in. and a base of 27 in.
what is the area of the flag?

Explanation:

4.

Step1: Calculate the area of the square

The formula for the area of a square is \(A = s^2\), where \(s\) is the side - length. Given \(s = 8\) in, then \(A_{square}=8\times8=64\) \(in^{2}\).

Step2: Find the area of the triangle (either side of the diagonal)

A diagonal of a square divides the square into two congruent right - triangles. The area of each triangle \(A_{triangle}=\frac{1}{2}A_{square}\).
Since \(A_{square}=64\) \(in^{2}\), then \(A_{triangle}=\frac{1}{2}\times64 = 32\) \(in^{2}\).

Step1: Use the formula for the area of a triangle

The formula for the area of a triangle is \(A=\frac{1}{2}bh\), where \(b\) is the base and \(h\) is the height.
Given \(b = 27\) in and \(h=12\) in.

Step2: Substitute the values into the formula

\(A=\frac{1}{2}\times27\times12\). First, calculate \(27\times12 = 324\). Then \(\frac{1}{2}\times324=162\) \(in^{2}\).

Answer:

The area on either side of the diagonal is \(32\) \(in^{2}\).

5.