SA = 2lw + 2lh + 2hw
SA = 2(15)(2) + 2(15)(6) + 2(6)(2)
SA = 60 + 180 + 24
SA = 264
Answer:
Equilateral triangle will always have a perpendicular bisector that is also an angle bisector.
Step-by-step explanation:
Equilateral triangle property:
- All sides of the equilateral triangle are equal.
- Angle of every equilateral triangle are equal to 60°.
- Every altitude of an equilateral triangle is also a median and a bisector.
- Each median is also an altitude and a bisector.
- Each bisector is also an altitude and a median.
Therefore, by equilateral triangle property;
Perpendicular bisectors are angle bisectors in an equilateral triangle Since, all sides and angles are the same in an equilateral triangle.
Also, the angle bisector of an equilateral triangle forms 90 degree angle with the opposite side and bisects that side.
Larger PyramidHeight 24 Volume 648
Pyramid Volume = (Area of the Base * Height) ÷ 3648 = Base Area * 24 / 3Base Area = 648 * 3 / 24Base Area = 648 / 8Base Area = 81Base Length = 9
a) The Scale Factor between the Small & Large PyramidLength - 3LATERAL Area - 9Volume - 27
Slant Height^2 = 4.5^2 + 24^2Slant Height^2 =
<span>
<span>
596.25
</span>
</span>
<span><span>Slant Height^2 = 24.4182308941
</span>
</span>
b)
Large Pyramid Area = (½ * Perimeter of Base * Slant Height) + Base AreaLarge Pyramid Area = (.5 * 36 * <span>24.4182308941) + 81
</span>Large Pyramid Area = 439.5281560938 + 81
Large Pyramid TOTAL Area =
<span>
<span>
520.5281560938
</span>
</span>
<span>Large Pyramid LATERAL Area =<span> 439.5281560938
</span>
</span>
**********************************************************************************c)
Smaller PyramidHeight 8Surface Area = 124
This pyramid has dimensions that are one third of the larger pyramid.Therefore, it has a base length of 3.Base Area = 9.
Its base perimeter would be 12.
Small Pyramid Volume = (Area of the Base * Height) ÷ 3Small Pyramid Volume = ( 9 * 8 ) / 3Small Pyramid Volume = 72 / 3
c) Small Pyramid Volume =24 cubic meters
d) Ratio of larger pyramid volume to smaller pyramid volume648 / 24 = 27The reason? Volume is a 3 dimensional quantity. The Larger pyramid is 3 times larger in terms of the base measurement.9 meters vs 3 meters - a factor of 3When we compare volumes, we have to cube this factor.3^3 = 27
Source : http://www.1728.org/volpyrmd.htm
