Geometry help, please?

Question

Find the volume, to the nearest tenth, of a pyramid that is 6 feet tall and whose base is an equilateral triangle with sides each 10 feet long.

Answer 1

You first get the area of the triangle

to get the height, you divide the equilateral triangle into two right triangles.

you use the pythagorean theorem

a^2 + b^2 =c^2

5^2 + b^2= 10^2

25 +b^2= 100

b^2 = 75

B= 8.66 feet

to get the volume

V= (Base xHeight)/3

B= (8.66 x 10)/2 = 43.33 sqr ft

V= (43.33 x 6)/3

V= 86.66 cubic feet.

Answer 2

im telling your geometry teacher.

Answer 3

Volume of pyramid = (1/3)(Area of Base)(height)

V = (1/3)(B)(h)

B = area of equilateral triangle = (1/2)bh

B = (1/2)(10 ft)(h)

Solving for h:  h = 10 ft x cos 30 deg = 8.66 ft

Hence,

B = (1/2)(10 ft)(8.66 ft) = 43.3 ft^2  

V = (1/3)(43.3 ft^2)(6 ft) = 86.6 ft^3    ANSWER

Hope this helps.

teddy boy