A regular square pyramid has base edge of 20 mm and total area 1,440 mm^2.
a) Find the slant height of the pyramid
b) Find the height of the pyramid
c) What is the volume of the pyramid
A regular square pyramid has a base edge of 20 mm and total area of 1440 mm2.
The area of the base is 20 mm x 20 mm = 400 mm2
Subtracting this from the total area gives an area of 1440 mm2 - 400 mm2 = 1040 mm2 for the sides.
Since there are four congruent triangles for the sides, each triangle will have 1040 mm2 / 4 = 260 mm2.
The area of each of these triangles can be found by the formula: Area = ½ · base · height.
Placing the values into this formula: 260 mm2 = ½ · 20 mm · height ---> height = 26 mm.
This is the slant height of the pyramid.
To find the height of the pyramid, draw a right triangle from the peak down to the middle of the base (side a = unknown height) to tme middle of one of the sides (side b = 10) and back up to the peak (the hypotenuse = 26)
Using the Pythagorean Theorem: a2 + 102 = 262 ---> a = 24 mm
This is the height of the pyramid.
Volume of the pyramid: V = (1/3) · (Area of the Base) · (Height of the Pyramid)
V = (1/3) · (400 mm2) · (24m) = 3200 mm3