The area of a regular hexagon is 1500 square centimeters. What is its perimeter? Please show working.

Question

The area of a regular hexagon is 1500 square centimeters. What is its perimeter? Please show working.

2 Answers

Impact of this question

2984 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-11-24T10:17:28

The perimeter is approximately $144.24 c m$ $144.24cm$ .

Explanation:

A regular hexagon consists of 6 congruent equilateral triangles, so its area can be calculated as:

$A = 6 \cdot \frac{a^{2} \sqrt{3}}{4} = 3 \cdot \frac{a^{2} \sqrt{3}}{2}$ $A=6*(a^2sqrt(3))/4=3*(a^2sqrt(3))/2$ .

The area is given, so we can solve an equation:

$3 \cdot \frac{a^{2} \sqrt{3}}{2} = 1500$ $3*(a^2sqrt(3))/2=1500$

to find the length of the hexagon's side

$3 \cdot \frac{a^{2} \sqrt{3}}{2} = 1500$ $3*(a^2sqrt(3))/2=1500$

Multiplying by $2$ $2$

$3 \cdot (a^{2} \cdot \sqrt{3}) = 3000$ $3*(a^2*sqrt(3))=3000$

Dividing by $3$ $3$

$a^{2} \cdot \sqrt{3} = 1000$ $a^2*sqrt(3)=1000$

For further calculations I take approximate value of $\sqrt{3}$ $sqrt(3)$

$\sqrt{3} \approx 1.73$ $sqrt(3)~~1.73$

So the equality becomes:

$1.73 \cdot a^{2} \approx 1000$ $1.73*a^2~~1000$

$a^{2} \approx 578.03$ $a^2~~578.03$

$a \approx 24.04$ $a~~24.04$

Now we can calculate the perimeter:

$P \approx 6 \cdot 24.04$ $P~~6*24.04$

$P \approx 144.24$ $P~~144.24$

Answer 2 · 2015-11-24T10:23:51

$perimeter = 144.17 cm$ $"perimeter"=144.17"cm"$

Explanation:

The hexagon can be split into 6 equilateral triangle.

Each triangle has area of $\frac{1500 {cm}^{2}}{6} = 250 {cm}^{2}$ $frac{1500"cm"^2}{6}=250"cm"^2$

If the length of each triangle is $l$ $l$ , then the perimeter of the hexagon is simply $6 l$ $6l$ .

Looking at 1 triangle, the area is given by half x base x height.

The base is $l$ $l$ . The height is found by cutting the triangle into half and applying Pythagoras theorem.

$h^{2} + {(\frac{l}{2})}^{2} = l^{2}$ $h^2+(l/2)^2=l^2$

$h = \frac{\sqrt{3}}{2} l$ $h=sqrt(3)/2l$

$Area = \frac{1}{2} \cdot l \cdot h$ $"Area"=1/2*l*h$

$= \frac{1}{2} \cdot l \cdot \frac{\sqrt{3}}{2} l$ $=1/2*l*sqrt(3)/2l$

$= \frac{\sqrt{3}}{4} l^{2}$ $=sqrt(3)/4l^2$

$= 250 {cm}^{2}$ $=250"cm"^2$

$l = 24.028 cm$ $l=24.028"cm"$

$perimeter = 6 l = 144.17 cm$ $"perimeter"=6l=144.17"cm"$

Science

Math

Humanities

... and beyond

The area of a regular hexagon is 1500 square centimeters. What is its perimeter? Please show working.

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question