Atriangular pyramid has a slant height of 13 inches. the triangular base has a perimeter of 23 inches and an area of 15 square inches. find the surface area show the work so that i understand it. also hurry as i need the answer soon.

A triangular pyramid has a triangle as its base and three triangle faces. 
since we are asked to find the surface area of the triangular pyramid, we have to find the area of all three triangle faces and the base.

area of the base is given - 15 square inches
triangular face area - 1/2 x height x length 
height of the triangle face is slant height - 13 inches

lets name the triangle faces as a,b and c
lets name the sides of the base triangle as A, B and C respectively
these sides are the lengths of the triangular faces.
area of face a - 1/2 * 13 inches * A
                    b - 1/2 * 13 * B
                    c - 1/2 * 13 * C
total area of the faces - (1/2 *13 * A) + (1/2 *13 * B) + ( 1/2 *13 * C)
                                    = 1/2 * 13 (A+B+C)
A+ B+C = total perimeter of the base = 23 inches 

therefore total surface area = area of base + total area of triangle faces
                                            = 15 + (1/2 * 13 * 23)
                                            = 15 + 149.5
total area = 164.5 sq.inches

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