Please walk me through how to do this.

Question

A pentagonal pyramid has a lateral area of 300 in2, where the perimeter of the base is 40 in. Determine slant height.

Answer 1

1) Divide perimeter of base by the number of sides --> length of side of base

2) Divide lateral area by number of sides -> area of a triangular face

3) Area of face is equal to (1/2) (length of side of base) ("height" of triangular face along surface) --> "height" of triangular face.

4) It's an isosceles triangle and the "height" along the face bisects it, therefore the slant height is the hypotenuse of the triangle with legs equal to this "height" and half of the base side length from (1). Use Pythagorean Theorem.

Hope that helps.

Answer 2

lateral surface area of pyramid = perimeter of base multiple slant height\2

given lateral surace area 300, perimeter of base 40.

then slant height =2multiple are of pyramid\perimeter of base

so slant height = 2*300\40=15

i hope that helps