Question

soon-yis house has a hexagonal window made up of six identical equilateral triangles as shown in the picture. which expression is equivalent to the area of one triangular section?
$\frac{1}{2}\times7\times8$
$\frac{1}{2}\times7\times7$
$\frac{1}{2}\times14\times16$
$\frac{1}{6}\times14\times16$

Explanation:

Step1: Recall the area formula for a triangle

The area formula for a triangle is \( A=\frac{1}{2}\times base\times height \).

Step2: Identify the base and height of the triangular section

From the problem, the base of each triangular section is \( 14 \) inches. The height of each triangular section is \( \frac{16}{2}=8 \) inches.

Step3: Substitute the values into the formula

Substitute \( base = 14 \) and \( height = 8 \) into the formula \( A=\frac{1}{2}\times base\times height \). We get \( A=\frac{1}{2}\times14\times8 \). Since \( 8 = 7\times\frac{8}{7}\), and simplifying \( \frac{1}{2}\times14\times8=\frac{1}{2}\times7\times2\times8=\frac{1}{2}\times7\times16\) (using commutative and associative properties of multiplication).

Answer:

\(\frac{1}{2}\times7\times8\)