Answer:
MA = 30
MR = 30 sqrt(2)
SA = 2400
Step-by-step explanation:
Call the point at the bottom of the altitude Q
We can find QS by using the Pythagorean Theorem
a^2+b^2 = c^2 where the legs are PQ and QS and the hypotenuse is PS
20^2 + QS^2 =25^2
400 + QS^2 = 625
Subtracting 400 from each side
QS^2 =225
Taking the square root of each side
QS = 15
Doubling this length is the distance across the square
2QS = 2*15 = 30
This is the distance MA = 30
We can use the Pythagorean theorem again to find MR
a^2+b^2 = c^2 where the legs are MA and AR and the hypotenuse is MR
MA = 30 and AR =30 since this is a square
30^2 + 30 ^2 = MR^2
900+900 = MR^2
1800= MR^2
Taking the square root of each side
sqrt(1800)= sqrt(MR^2)
30 sqrt(2) = MR
surface area of a square pyramid is the area of the base + the area of the side times fours (since we have 4 identical sides)
area of the base is MA*AR = 30*30 = 900
The area of the side is 1/2 bh since it is a triangle
1/2 (AR) (PS) = 1/2 (30) 25) =375
Multiply this by 4 since we have 4 sides
375*4 =1500
Add this to the base
1500*900 =2400
