Calculate Hexagon Area with 28 cm² Rectangle Inside: Geometry Problem

Question

Below is a hexagon that contains a rectangle inside it.

The area of the rectangle is 28 cm².

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What is the area of the hexagon?

Video Solution

Solution Steps

00:00 Find the area of the hexagon
00:03 We'll use the formula for calculating rectangle area (side times side)
00:06 We'll substitute appropriate values according to the given data and solve for A
00:09 We'll isolate A
00:13 This is the side in the rectangle, which is also the side in the regular hexagon
00:20 In a regular hexagon all sides are equal
00:25 We'll use the formula for calculating the area of a regular hexagon
00:34 We'll substitute the side value and solve for the area
00:42 We'll simplify what we can
00:48 And this is the solution to the question

Step-by-Step Solution

Since we are given the area of the rectangle, let's first work out the length of the missing side:

7×a=28 7\times a=28

We'll now divide both sides by 7 to get:

a=4 a=4

Since all sides are equal in a hexagon, each side is equal to 4.

Now let's calculate the area of the hexagon:

6×a2×34 \frac{6\times a^2\times\sqrt{3}}{4}

6×42×34 \frac{6\times4^2\times\sqrt{3}}{4}

Finally, we simplify the exponent in the denominator of the fraction to get:

6×4×3=24×3=41.56 6\times4\times\sqrt{3}=24\times\sqrt{3}=41.56

Answer

41.56