i have 18.8?

Question

The slant height of a square pyramid is 25cm. Find the height if the base edges are 14cm.

Answer 1

The slant height, height and half the diagonal form together a right triangle. Since the base is 14 cm each side, the diagonal will be 14*sqrt(2) and half this will be 14/sqrt(2).
Since the slant height is the hypotenuse for this triangle, the height of the pyramid will be sqrt(25^2 - (14/sqrt(2))^2) = sqrt(625 - 98) = sqrt(527) = 22.96 cm

Answer 2

NICE PROBLEM !

I make the height of the pyramid 24cm. Here's how:

"Slant height" is not a conventional geometric term, but I take it to be the distance from the MIDPOINT of one side of the BASE to the VERTEX.

Look at a triangle made up of the vertical height from the CENTRE of the SQUARE BASE to the VERTEX, of length ' h ' cm, the "SLOPING HEIGHT" line, length 25 cm, and the line joining the MIDPOINT of a side of the BASE to the CENTRE of the square BASE, of length 7 cm.

This is a right-angled triangle with hypoteneuse 25 cm and base length (one of the two perpendicular sides) of length 7 cm. Since 7 and 25 belong in a classic Pythagorean triple (7, 24, 25) with 25 being the hypoteneuse, as here, the height ' h ' is 24 cm.

(In other words, 25^2 - 7^2 = 625 - 49 = 576 = 24^2.)

It seems that this problem was a quick exercise in recognizing a classic Pythagorean triple in an unusual setting.

Live long and prosper.

Answer 3

I got 24 as well

slant height^2= (1/2Base Length)^2+ Height^2

pythagorean theorem