Question

this diagram shows a regular hexagon. what is the area of regular hexagon abcdef? type your answer in the box. square units

Explanation:

Step1: Calculate the area of the large rectangle

The length of the large rectangle is \(15 + 30+15=60\), and the width is \(26 + 26 = 52\).
The area of a rectangle is \(A=\text{length}\times\text{width}\), so \(A_{rectangle}=60\times52\).

$$A_{rectangle}=3120$$

Step2: Calculate the area of the four right - angled triangles

Each right - angled triangle has legs \(a = 15\) and \(b = 26\).
The area of a right - angled triangle is \(A_{\triangle}=\frac{1}{2}ab\).
Since there are 4 such triangles, \(A_{4\triangle}=4\times\frac{1}{2}\times15\times26\)

$$A_{4\triangle}=2\times15\times26 = 780$$

Step3: Calculate the area of the hexagon

The area of the hexagon \(A_{hexagon}=A_{rectangle}-A_{4\triangle}\)

$$A_{hexagon}=3120 - 780$$

$$A_{hexagon}=2340$$

Answer:

\(2340\)