Question

What is the area of the shaded region below? Assume the hexagon is regular. Use your calculator and round your final answer to the nearest hundredth.

Answer 1

You need to calculate the area of the six sided polygon and then take the area of the rectangle from that, do you remember how to calculate those areas?

Answer 2

not really :/

Answer 3

463.86 sq units

Answer 4

The area of the triangle is its base times its height, and the figure has 6 triangles, so what you have to do is to calculate the area of one of them and then multiply it by 6. The figure is divided in six triangles, so each triangle covers 60° of the circle and all the sides of the triangle are equal. With that in mind we see that the area of each triangle is\[2\frac{l^2 \cos(30°)}{4}=\frac{l^2 \sqrt{3}}{4}\]So the total area is \[\frac{3l^2\sqrt{3}}{2}\]In your problem we have to take of the area of the rectangles so it becomes:\[\frac{3l^2\sqrt{3}}{2}-lb=\frac{3\times18^2\sqrt{3}}{2}-18\times21=463...\]So you are correct.