Help Quickly: Geometry Puzzles

Dan-O

I am involved in an online game of Suvivor on a message board I frequent which a few Canadians are running. The latest challenge is an individual challenge and its geometry. I'm usless....can anyone help?

1) Consider the parallelogram ABCD with AD parallel to BC and AB parallel to DC. The bisector of the angle ABC intersects AD at E. Determine AB, given that ED = 5, BE = 6 and CE = 6.

2) The areas of three of the six rectangular faces on a cuboid box are 160 cm², 120 cm², and 145 cm². What is the volume of the box?

3) What is the area of the triangle DEF if the lengths of the altitudes are 4, 5, and 6?

4) If the volume of a cone is three times the area of its base, what is the height of the cone?

Pines

Not sure if you need the worked solution or just the answers.

Dan-O wrote:

2) The areas of three of the six rectangular faces on a cuboid box are 160 cm², 120 cm², and 145 cm². What is the volume of the box?

If the length, breadth and depth are x, y and z
xy=160 and yz=120 and xz=145

xy*yz*xz = (xyz)^2 = volume squared

therefore volume = square root of (160 * 120 * 145) = 1668.532 cm3 (approx!)

Dan-O wrote:

4) If the volume of a cone is three times the area of its base, what is the height of the cone?

Volume, V = (1/3) * pi * r² * h
Area of base, A = pi * r²
so V = (1/3)* A * h
and we're told that V = 3A

so 3A = (1/3)* A * h
9A = A * h
h = 9