Do you know your geometry?
Geometry
Level
pending
The base of a pyramid is a rhomboid. If a=5cm d1=6cm and the larger diagonal intersection is an equilateral triangle, calculate the volume of the pyramid.
32sqrt2 cm3
32sqrt3 cm3
27cm3
4sqrt3 cm3
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
If the larger diagonal intersection is an equilateral triangle, then the larger diagonal of the rhomboid is equal to the side line. We then calculate the larger diagonal which is later used for calculating the height of the pyramid. The formula for the longer diagonal is 2sqrt a^2-(d1/2)^2. The longer diagonal is 8cm. For calculating the volume, we will need the base (the area of the rhomboid) and the height of the pyramid. The height is calculated with the formula sqrt s^2-(d2/2)^2. Because the larger diagonal intersection is an equilateral triangle, we can come to the conclusion that s=d2. The height is 4 sqrt3 cm. The base is calculated with the formula d1 d2/2 (24cm^2), and the formula for the volume is B H/2 where the B is the base area and H is the height of the pyramid. The final solution is 32 sqrt3.