Geometry Question Part B?

Question

Ok here is the 2nd part:

ABCDEFGH is a cube having a side length of 2. P is the midpoint of EF, as shown (through link). Determine the area of triangle ABP.

http://i58.photobucket.com/albums/g254/poker5495/POWII-1.jpg

10 points will go to the correct and best answer. If you can show me steps on getting the answer I really appreciate it.

Answer 1

The area of a triangle is

(1/2)(base)(height)

b = base = 2

The height of the triangle is the same as the diagonal of a face of the cube.

h = 2√2

So the area of the triangle is:

A = (1/2)(2)(2√2) = 2√2

Answer 2

The answer is 3. Use pythagorean theorem twice. Once to find the base of the diagonal trianlge....that side is sqrt 5. Then you have a triangle with leg 2, and leg sqrt 5. That gives you a hypotenuse (the diagonal in question) of 3.

Answer 3

Assuming T is the top area of the perspective, and ok is the decrease: Draw a line section between T and ok. (word: This purely works if TK is perpendicular to the coolest line) perspective KTD(vertex T) is ninety-38=fifty two levels perspective DKT(vertex ok) is90-31=fifty 9 levels upload up the measures:fifty two+fifty 9=111 levels one hundred eighty-111=sixty 9 levels