If a prism has equilateral triangle bases with side lengths of 4 cm. The height of the prism is 8 cm.?

Question

So what's the volume?

Answer 1

To find the triangle's height...

4^2 = (2)^2 + h^2
16 = 4 + h^2
12 = h^2
h = 2 sqrt 3

So the area of the base (triangle) is
(1/2)(2 sqrt 3)(4)
= 4 sqrt 3

The volume is (area of base) x (height)
(4 sqrt 3)(8)
= 32 sqrt 3

Answer 2

efficient: the quantity for any prism is V = BH, the situation B represents the portion of the backside and H represents the precise of the prism. on your triangular prism, the bases of the prism are ideal triangles. In a ideal triangle, the section is a million/2 bh, the situation b is the backside of the triangle and h is the precise of the triangle. putting this all on the comparable time, you get V = BH V = a million/2 (6)(8) x (12) V = 24 (12) V = 288 cubic instruments. the exterior section is purely the portion of the areas that make up the prism. on your prism, 2 triangles - a million/2 (6)(8) = 24, so 2 of them cover 40 8 sq. instruments. a million rectangle - 6 (12) = seventy 2 sq. instruments. a million rectangle - 8 (12) = ninety six sq. instruments. a million rectangle 10 (12) = one hundred twenty sq. instruments. (The portion of the 0.33 rectangle is 10, by fact of Pythagorean Theorem.) Grand finished is 336 sq. instruments.

Answer 3

The area of a triangle is 1/2 bh. You already know b; that's 4 cm. Since the angle is 60 deg, the height will be 4 * sin(60) or 2*sqrt(3). Area of the triangle base then is 1/2*4*2*sqrt(3) = 4*sqrt(3). Height is 8 cm, so the volume is 8*4*sqrt(3) = 32*sqrt(3).

Answer 4

The area of the equilateral base is 4 x root3 square centimeters (approximately 6.923 sq cm). Multiply by the height of the prism, to get an enclosed volume of approximately 55.426 cubic cm.

Answer 5

V = h * B

Volume = Height * Area of Base

K = a^2sqrt(3)/4
Area = (4)^2 * sqrt(3)/4
Area = 4sqrt(3)

V = 4sqrt(3) * 8
V = 32sqrt(3)cm^3

ANS : about 55.4256cm^3