Can someone please help, I need this done soon :))
A square pyramid has a height of 18 cm. A side length of the base of 11 cm. What is the volume of the pyramid?

cm3

The volume of the pyramid is

Explanation:

The height of the square pyramid is 18 cm

The base of the square pyramid is 11 cm

The volume of the square pyramid can be determined using the formula,

Substituting and in the formula, we have,

Simplifying, we have,

Multiplying, we get,

Dividing, we get,

Thus, the volume of the pyramid is

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!