*PLEASE HELP WITH STEP BY STEP WORK!*

#1: What is the perimeter of the triangle? *
A. 8 inches
B. 8 sqrt 3 inches
C. 4 sqrt 3 inches
D. 24 sqrt 3 inches

#2:
a. What is the area of the figure in square feet? Exact answer only. No units.

b .From Question #2, What is the side length of the figure? *
A .10 feet
B. 10 sqrt 2 feet
C. 5 sqrt 2 feet
D. 5 sqrt 3 feet

#3: What is the length of the apothem? *
15 cm
30 cm
15 sqrt 3 cm
7.5 sqrt3 cm

#4: What is the area of the figure? *
A. 12,150 sqrt 3 square meters
B. 25,300 sqrt 3 square meters
C. 12,150 square meters
D. 1,950 sqrt 3 square meters

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.