A regular hexagon has a perimeter of 48 cm. Find its area. (Use the formula A = 3√3/2 a^2, where a is the side length.)

A regular hexagon has a perimeter of $48$ cm. Find its area. (Use the formula $A = \frac{3 3}{2} a^{2}$ , where $a$ is the side length.)

hard 3 marks Class 5 · Mathematics · Shapes and Angles

Answer

96\sqrt{3} cm^2

The correct answer is 96\sqrt{3} cm^2 — Multiply the constants: $3 \times 32 = 96$ , so $A = 963$ cm $^{2}$ .

Determine the side length from the perimeter: $P er im e t er = 6 a$ , so $a = \frac{48}{6} = 8$ cm.
Substitute $a$ into the area formula: $A = \frac{3 3}{2} a^{2}$ .
Compute $a^{2} = 8^{2} = 64$ .
Multiply: $A = \frac{3 3}{2} \times 64 = \frac{3 3 \times 64}{2}$ .
Simplify the fraction: $64/2 = 32$ , giving $A = 33 \times 32$ .
Multiply the constants: $3 \times 32 = 96$ , so $A = 963$ cm $^{2}$ .

Common mistake: Forgetting to divide the perimeter by 6 to get the side length or miscalculating the multiplication

Concept tested: Area of regular hexagon