SOLUTION: Find the total surface area of a square-based pyramid with isosceles triangular faces.

Question 54113: Find the total surface area of a square-based pyramid with isosceles triangular faces.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Find the total surface area of a square-based pyramid with isosceles triangular faces.
LET THE SQUARE SIDE = B.....
LATERAL SURFACE AREA =L.S.A.
CASE 1 ...........SLANT SIDE IS GIVEN
LET THE SLANT SIDES OF TRIAGULAR FACES = D
LATERAL SURFACE AREA = 4 * TRIANGLE AREA =4*0.5*BASE*SLANT HT.
SLANT HT = SQRT(D^2-B^2/4)
HENCE L.S.A.= 2*B*SQRT(D^2-B^2/4)
CASE 2....SLANT HEIGHT IS GIVEN = H
L.S.A=2BH
CASE 3.....VERTICAL HEIGHT IS GIVEN...= V SAY
THEN SLANT HEIGHT = SQRT(V^2+B^2/4)
L.S.A. = 2*B*SQRT(V^2+B^2/4)
BASE AREA
BASE AREA = B^3
TOTAL SURFACE AREA
T.S.A. = L.S.A.+B.S.A....FOUND ABOVE
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