Question

i need help on this pleasea) each dashed line is a (write the name not the measurement)b) the red line segnment is the (write the name not the measurement )c) there are _ congruent triangles in a regular hexagond) the measurement of the radius of the hexagon=_e) the perimeterthe apothem=_ rounden to the nearest tenth)the area= _(use the rounded apothem)

Answer 1

Answer: The area of the hexagon is 261 square centimeters

To calculate the area of the of regular hexagon, we need to find the apothem first

Step 1: find the apothem

To find the apothem, we will be applying the pythagora theorem

The above triangle can be split into two

The hypotenus of the triangle is the same as the side of the hexagon

`\begin{gathered} \text{Pythagora's theorem} \\ \text{Hypoyenus}^2=opposite^2+adjacent^2 \\ \text{Hypotenus = c, opposite = a, and adjacent = b} \\ 10^2=5^2+a^2 \\ 100=25+a^2 \\ \text{Collect the like terms} \\ a^2\text{ = 100 - 25} \\ a^2\text{ = 75} \\ \text{Take the square root of both sides} \\ \text{a = }\sqrt[]{75} \\ \text{a = }8.7cm \end{gathered}`

apothem = s / 2 tan (180/n)

let s = length of the side

n = number of sides

Step 2: find the area using the calculated apothem

Area = 1/2 x perimeter x apothem

Perimeter = 6a

a = 10cm

Perimeter = 6 x 10

Perimeter = 60cm

Area = 1/2 x 60 x 8.7

Area = 30 x 8.7

Area = 261 square centimeters

Therefore, the area of the hexagon is 261 square cm