Dragan

1)  Calculate angles   DAC  and  DBM     ( ∠DAC = ∠MNC = ∠ENB )    ( ∠DBM = ∠EBN )

2)  Find line segments     MN  and  BN

3)  Find the area of a triangle  BNC

4)  Find the area of a triangle  BEN  using the law of sines and Heron's formula.

Add these two areas ( BNC and BEN ) and you're done.  

( Btw, the above post is mine too)

Given that point O is the center of the circle and OA=5, OC=8, and angle ACO=30∘, find cos(angle BOA). 

Use the Law of cosines to calculate side AC and the angle OAB.

∠OAB = ∠OBA

∠BOA = 180º - ( ∠OAB + ∠OBA )  

Angle bisectors AX and BY of triangle meet ABC at the point I. Find angle C in degrees, if angle AIB = 109.

Angle C = 38º   

The bases of an isosceles trapezoid have lengths that differ by 30. The two legs of the trapezoid
have length 25, and the two diagonals of the trapezoid have length 52. What is the area of the
trapezoid?

Let ABCDEFGH be a rectangular prism, where EF = 4, EH = 5, and EA = 6. Find the volume of the pyramid CFAH.

All the sides (including the base) are congruent.

The lengths of the sides are:    ( ≈ )    6.403,     7.211,     and      7.81

Area of the base                A ≈ 21.6564 u²

Height of the pyramid         h ≈ 5.5456

The volume of the pyramid CFAH             V = 1/3 * Ah ≈ 40.033 u³   

RQ = sqrt(6)  

ABCDE is a pentagon with the sum of interior angles of 540º.

∠ABC+∠CDE = 270º    

Bravo, thelizzybeth!!! Your method is very good, and your answer is a 100% correct!!! 

Nope, it cannot be 80!!! 

A = ( 5² + 4² + 3² ) - 1/2 ( 5 * 12 ) = 20 

  r = sqrt( 2 * 5² ) = 7.071067718

  A  = r² pi =  50*pi = 157.0796327 units squared