First slide

Equation of line in Straight lines

Question

Area of the regular hexagon whose diagonal joins (2, 4) and (6, 7) is

Moderate

A

$\frac{75 \sqrt{3}}{8}$
B

$\frac{7 \sqrt{3}}{16}$
C

$\frac{6 \sqrt{3}}{16}$
D

$\frac{25 \sqrt{3}}{16}$

Solution

We have A(2,4) and 8(6,7) as end points of diagonal of the hexagon.
$∴ A B = 5$
So, length of the line segment joining centre of the hexagon and one of the vertices is $\frac{5}{2}$
$∴ Area of hexagon = 6 \times Area of equilateral triangle having side length \frac{3}{2}$
$\begin{aligned} = 6 \times \frac{\sqrt{3}}{4} \times \frac{25}{4} \\ = \frac{75 \sqrt{3}}{8} \end{aligned}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App