Which statement is true about these triangles?
a. triangle pqr is similar to triangle def

b. triangle mno is similar to triangle pqr

c. triangle pqr is similar to triangle ghk

d. triangle mno is similar to triangle ghk

D. Triangle MNO is similar to Triangle GHK

Step-by-step explanation:

We know that the sum of the interior angles of a triangle is 180 degrees.

To identify similar triangles, we must look for triangles what share the same combination of interior angles.

Triangle MNO has has known angles of 79 and 22 degrees, which leaves (180 - 79 - 22) 79 degrees for the unknown angle, so two angles of 79 degrees and one of 22 degrees.

We see that DEF has an angle of 82 degrees... so it's not similar.

Triangle PQR has an angle of 20 degrees... so it's not similar either.

Triangle GHK has two known angles of 79 degrees... we know that the unknown is 22 degrees (because the total needs to be 180).

So, both GHK have 2 angles of 79 degrees and one angle of 22 degrees... they are then similar.

Regular polygon area = n*side^2 / (4 * tan (180/n))
where "n" is number of sides
The formula is dependent on the side^2 term,
So, if we have an octagon that has sides 4 times as large, that means the area will be sixteen times larger.
side^2 = 4^2 = 16
So we multiply 25 cm^2 by 16 and we get
400 square centimeters.

Source:
http://www.1728.org/polygon.htm