Question

2. Find the area of the regular polygon. Give the answer to the nearest tenth. Hexagon with a radius of 5 in.

A. 65.0 in.^2
B. 129.9 in.^2
C. 259.8^2
D. 53.0^2

3. Divers looking for a sunken ship have defined the search area as a triangle with adjacent sides of length 2.75 miles and 1.32 miles. The angle between the sides of the triangle is 35°. To the nearest hundredth, find the search area.
A. 2.08 mi.^2
B. 2.97 mi.^2
C. 1.49 mi.^2
D. 1.04 mi.^2

Answer 1

`360 / 6 = 60 \\ 60 / 2 = 30 \\ (1)/(2) (2.5 √(3) )(5) \\ 6(6.25 √(3) ) = 65.0`
Answer for #2 is A

3. D

Answer 2

Answer: The correct options are (2). A, (3). A.

Step-by-step explanation: The calculations are as follows:

(1) We are to given the area of a regular hexagon with radius 5 in.

The AREA of a regular hexagon with side 'a' units is given by

`A=(3\sqrt3)/(2)a^2.`

We know that the radius of a regular hexagon is equal to the length of each side, so we have

a = 5 in.

Therefore, the area of the hexagon will be

`A=(3\sqrt3)/(2)* 5^2=1.5* 1.732* 25=64.95\sim 65~\textup{in}^2.`

Thus, (A) is the correct option.

(2) Given that two adjacent sides of the triangle measure 1.32 miles and 2.75 miles.

The angle lying between the two sides measure 35°.

we are to find the area of the triangle.

We know that the area of a triangle with two adjacent sides of measure 'a' and 'b' units and 'β' be the measure of the angle lying between them is given by

`A=(1)/(2)ab\sin \beta.`

Here, a = 2.75 miles, b = 1.32 miles and β = 35°.

Therefore, the total search area, in the form of triangle is given by

`A=(1)/(2)* 2.75* 1.32* \sin 35^\circ=1.815* 0.5735=2.08~\textup{mi}^2.`

Thus, the correct option is (A) 2.08 mi².

Hence, the correct options are (2). A, (3). A.