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# help

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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

Apr 28, 2020

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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

Apr 28, 2020