Question

2. Find the measure of each numbered angle

16. Find the area with the given radius or apothem. If your answer is not an integer leave it in simplest radical form.

Answer 1

2.
Assume the quadrilateral is a square.
Then m<4 = 90
m<5 = 45
m<6 = 45

16.
Assume it's a regular hexagon.
The hexagon can be divided into 6 congruent equilateral triangles.
The 3 sides of each equilateral triangle measures 6sqrt(3) m.
When you draw a segment from the center of the hexagon to a side of the hexagon, you divide one of the 6 triangles into 2 30-60-90 triangles. The ratio of the lengths of the sides of a 30-60-90 triangle is 1 : sqrt(3) : 2. That segment is also the height of one of the 6 triangles.
height = (6sqrt(3))/2 * sqrt(3) = 9
Now we know the base and height of one of the 6 triangles.The area of the hexagon is 6 times the area of one triangle.

area of hexagon = 6 * bh/2
area of hexagon = 6 * 6sqrt(3) m * 9 m/ 2 = 324sqrt(3) /2 m^2 = 162sqrt(3) m^2

Answer 2

2) 4 = 90
5 = 45
6 = 45

16) this one's a bit long :)

PLEASE READ
I MADE A DUMB MISTAKE WHEN WORKING OUT THE HEIGHT
ITS NOT 8.41 ITS 9
SORRY ABOUT THAT