Question

1.) Find the area of a regular hexagon with an apothem 10.4 yards long and a side 12 yards long. Round your answer to the nearest tenth.

My answer: 312square yards. Is that correct?

2.) Question is: A park in a subdivision is triangular-shaped. Two adjacent sides of the park are 533 feet and 525 feet. The angle between the sides is 53 degrees. Find the area of the park to the nearest square foot.

My answer: 111739.09. Is that correct?

Answer 1

find the area of each of the 6 equilateral triangles making up the hexagon

Each side of triangle = 12 yards

{ by the way, first check apothem length because it is our altitude )
tan 30 = (1/2)(12)/apothem
apothem = 6/tan 30 = 10.4 - sure enough, whew }

so area of triangle = (1/2)(base)(apothem)
= .5 * 12 * 10.4 = 62.4

so 6 of them is 6*62.4 = 374 yd^2

Answer 2

That's what i got

Answer 3

= 111739 square feet

Answer 4

Thats i got for the second one.

Answer 5

U r correct for the second one. But i got a different answer for the first one

Answer 6

Alright. Thank you.

Answer 7

How did you get the second one?

Answer 8

@rhr12

Answer 9

Area = (1/2)(533 ft)(525 ft) sin(53) = 111739 square feet

Answer 10

Alright. Thank you

Answer 11

@Michele_Laino is this information correct?

Answer 12

that rhr put

Answer 13

question #1
perimeter=6*12=72 yards, so:

\[\Large \begin{gathered}
area = \frac{{perimeter \times apothem}}{2} = \hfill \\
\hfill \\
= \frac{{10.4 \times 72}}{2} = 374.4 \hfill \\
\end{gathered} \]

Answer 14

question#2
the requested area is:
\[\Large Area = \frac{1}{2} \times 533 \times 525 \times \sin 53 = 111,739.0907\]

Answer 15

so, the second answer is correct!