Geometry Volume Question

If the surface area of a square pyramid is 300 m, and the sides of the base measure is 10m then find the height of the pyramid. Help please?

Assuming you mean the area is 300 m² since "m" is a linear measure and cannot represent a measure of area:

The base has area 10*10 = 100, leaving 300-100 =200 to be the area of the pyramid sides. Each side would have area = 200/4 = 50 m² = bs/2 = 5h ==> s = 10 m

Slant height of the pyramid is 10 m.
Height of the pyramid: h = √[s² - (b/2)²] = √(100 - 25) = √75 = 5√3

Height of the pyramid is 5√3 meters

Surface Area of Pyramid = s² + 2sl
l = slant height
s =side =10m
300 = 10^2 + 2x10xl
200 = 20l
l=10m
h^2 = l^2-s^2/4 = 100 - 25 =75
h=sqrt of 75 = 8.66 m

Square Pyramid Definition:
A Square Pyramid is a pyramid with a square base.

Square Pyramid Formula :
Area of Base(A) = s²
Surface Area of Pyramid = s² + 2sl = A + 2sl
Volume of Pyramid = (1/3)b²h
where
s,b = side, h = height and l = slant height
Square Pyramid Image/Diagram
big-square-pyramid
Square Pyramid Example :
Case 1: Find the surface area and volume of a square pyramid with the given side 3, height 4 and the slant height 5.

Step 1: Find the area of the base.
Area of the base(A) = s² = 3² = 9.

Step 2: Find the surface area of pyramid.
Surface Area of Pyramid = A + 2sl = 9 + (2 * 3 * 5) = 9 + 30 = 39.

Step 3: Find the volume of pyramid.
Volume of Pyramid = (1/3)b²h = (1/3)b²h = (1/3)* 3² * 4 = 0.33 * 9 * 4 = 12.

The above example will clearly illustrates how to calculate the Volume, Surface Area of a Square Pyramid manually.

Area of the base => A = s² = 100 m²
Surface Area => SA = s² + 2sl = A + 2sl
where: l = slant height
300 = 100 + 20*l
200 = 20*l => l = 10 m
h = √(100 - 25)
= √75 = 5√3 m