Dragan

 1)     A = n / 360° pi * r²              A = 90° / 360° * pi * 5²             A ≈  19.635 u²  

Number 2 works for   r = 1          A = n / 360° * pi * r         A = 90° / 360° * pi * 1        A ≈ 0.785 u°    

A = 360 / 360 * pi * 5²            A ≈ 78.539 u²         

There are 4 isosceles triangles:  ABD,  CDE,   BCE,  and   AEC.

Δ ABD  =>   45° + 67.5° + 67.5° = 180°

Δ CDE  =>   45° + 67.5° + 67.5° = 180°

Δ BCE  =>    45° + 90° + 45° = 180°

Δ AEC  =>    45° + 67.5° + 67.5° = 180°    

  Triangle   AEC  is an isosceles triangle, because 2 of its 3 angles are equal, and as a result of that, 2 of its sides are equal as well.            

ABC is an equilateral triangle with side length 4. M is the midpoint of BC, and AM is a diagonal of square ALMN. Find the area of the region common to both ABC and ALMN.

We answered this one several days ago, and the answer is still the same: Area ≈ 32 u²  

Partner A and B split their profits in a ratio of 2 : 3. If Partner A makes a profit of $2700, how much profit, in dollars, does Partner B make?

                      2 : 3 = 2700 : B              B = 4050  

"... and let D be the foot of the altitude from BC to. "    ?!?!? 

1) In acute triangle ABC, we know AB = 7, BC = 8, and that CA is the shortest side. What is the smallest possible integer value of CA?

The smallest possible integer value of CA is  4  

3) Two sides of an acute triangle are 8 and 15. How many possible lengths are there for the third side if it is an integer?

There are only 4 possible lengths and they are:  8, 9, 10 and 11  

A sector of a circle has a central angle of 100 degrees. If the area of the sector is 250pi, what is the radius of the circle?

Sector area:      A = 250pi                  100° : 250pi = 360° : X         X = 900pi

Sector angle:    q = 100°

Circle radius:     r = ?                            r = sqrt (900)       r = 30  

                                                            ( A = r²pi        A = 30²pi = 900pi )  

The area of the octagon is:   A ≈ 32 u²   

It was pretty bouncy, nevertheless, the distance that the ball has travelled was  40.00 ft