Question

Help me pls i ned this right noe

Answer 1

What I got was 64.95 cm??

Answer 2

Answer:

should be easy to calculate it yourself, I dont have a calculator nearby

Step-by-step explanation:

okay, so the most important thing to understand is, that you can split the hexagon into 6 regular triangles.

These triangles have 3 60° angles and all 3 sides are the same length (5cm).

So, to get the overall area you have to calculate 6 * <area fo the triangle>.

The area of the triangle is calculated by multiplying the length of one side and the height and then splitting that in 2. The height itself is calculated via Pythagoras.

ok lets get to calculating, im gonna call one side of 5cm a:

${a}^{2} = {\frac{a}{2}}^{2} + {h}^{2}$

${h}^{2} = { a}^{2} - { \frac{a}{2} }^{2}$

${h}^{2} = { a}^{2} - { \frac{ {a}^{2}}{4} }$

$\sqrt{ {h}^{2} = \frac{4{a}^{2} }{4} - { \frac{ {a}^{2}}{4} }}$

$h = \sqrt{\frac{ {3a}^{2} }{4} }$

$h = \frac{ \sqrt{3{a}^{2}} }{2}$

now we have the height and we can easily get the area of a single triangle:

$area \: t \: = \frac{a}{2} \times h \times \frac{1}{2}$

$t = \frac{a}{2} \times \frac{ \sqrt{3{a}^{2}} }{2} \times \frac{1}{2}$

$t = \frac{a \times \sqrt{3 {a}^{2} } }{2}$

bow we have a formula for your triangle and we just have to take it by 6 because our hexagon consists of 6 of these triangles:

$complete \: area = 3 \times a \times \sqrt{3 {a}^{2} }$

now you just put your 5 cm in for a and put the entire thing into a calculator. Is about 130 for me