Find the lateral surface area of
the following square pyramid:

Given:

A square base pyramid with base length 6 cm and the slant height is 4 cm.

To find:

The lateral surface area of the given square pyramid.

Solution:

The lateral surface area of the given square pyramid is equal to the areas of 4 congruent triangles with base 6 cm and height 4 cm.

Area of a triangle is:

So, the area of one triangle or one side of the given pyramid is:

Now, the lateral surface area of the given square pyramid is 4 times the area of one triangle.

Therefore, the lateral surface area of the given square pyramid is 48 cm².

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

answer: 8d

step-by-step explanation:

45+5= 50+5=55+5=60