Question

1. a regular hexagon is made of equilateral triangles as shown. what is the area in square centimeters of the regular hexagon? (the image shows a regular hexagon with side length 5 cm, and the height of one of the equilateral triangles (the apothem - related height) is 4.3 cm)

Explanation:

Step1: Find area of one equilateral triangle

The formula for the area of a triangle is $\frac{1}{2} \times base \times height$. Here, the base is $5$ cm and the height is $4.3$ cm. So, the area of one triangle is $\frac{1}{2} \times 5 \times 4.3 = 10.75$ $cm^2$.

Step2: Find number of triangles in hexagon

A regular hexagon is made up of $6$ equilateral triangles (as shown in the diagram).

Step3: Calculate area of hexagon

To find the area of the hexagon, we multiply the area of one triangle by the number of triangles. So, $10.75 \times 6 = 64.5$ $cm^2$.

Answer:

The area of the regular hexagon is $64.5$ square centimeters.