Right Triangular Prism
Author: Lewis Prisco

Use this worksheet to practice finding the Volume and Surface Area of a Triangular Prism.  Adjust the height_1, base, and height using the labeled sliders.  Answer the questions below.  The multi-colored switches can be used to check your work.

1.Find the volume and surface area for 5 different Right Triangular Prisms.

2. Find the missing dimesion. Round to the nearest unit.
a. Triangular Prism: volume 450cu ft, height_1 ___, base 9.5ft, height 7.8ft

b. Triangular Prism: surface area 165sq in, height_1 4.5in, base 7in, height ___, hypotenuse 6.5in

3. In a triangular prism, what is the difference between the height of the base and the height of the prism?

y

z

V=\frac{1}{2}(h_1)(b)(h)

S.A.=(2)( \frac{ 1 }{ 2 } )(h_1)(b)+(h_1)(h)+(h)(b)+(h)(c)

Solution for Surface Area

x

height_1 = 10 (slider from 1 to 10, step 0.1)
E = (14, 5)
F = (14, 6)
G = Dilate(F, height_1, E)
u = Vector(E, G)
H = (14, 3)
I = (15, 3)
J = (17, 6)
base = 10 (slider from 1 to 10, step 0.1)
height = 10 (slider from 1 to 10, step 0.1)
L = Dilate(I, base, H)
v = Vector(H, L)
g = Circle(J, height)
K = (16, 5)
h = Line(J, K)
M = Intersect(g, h, 1.0)
w = Vector(J, M)
A = (-4, 0)
B = Translate(A, v)
C = Translate(A, u)
P, b, c, a = Polygon(C, A, B)
C' = Translate(C, Vector[w / 2.0])
A' = Translate(A, Vector[w / 2.0])
B' = Translate(B, Vector[w / 2.0])
P', b', c', a' = Polygon(C', A', B')
Q, c_1, c'_1, a'_1, a_1 = Polygon(C, C', A', A)
R, c_2, b_1, b'_1, c'_2 = Polygon(C, B, B', C')
S, a_2, a'_2, b'_2, b_2 = Polygon(A, A', B', B)
D = Midpoint(C, A)
N = Midpoint(A, B)
O = Midpoint(B, B')
T = Midpoint(C, A)
U = Midpoint(A, B)
V = Midpoint(B, B')
SurfaceAreaSolution = 0 (slider from 0 to 1, step 1)
W = (13.200000000000001, 11.9)
Y = (12.350000000000001, 9.25)
Z = (12.950000000000001, 6.3500000000000005)
A_1 = (12.8, 3.75)
E_1 = If(SurfaceAreaSolution ≟ 1.0, A_1)
v_1: 1.0 / 2.0 * height_1 * base * height
T5: v_1 + "= \frac{ 1 }{ 2} (" + height_1 + ")(" + base + ")(" + height + ")"
q_1: sqrt(height_1^(2.0) + base^(2.0))
F_1 = Midpoint(B', C')
s_1: height_1 * base + height_1 * height + height * base + height * q_1
T8: s_1 + "=(2)( \frac{ 1 }{ 2 } )(" + height_1 + ")(" + base + ")+(" + height_1 + ")(" + height + ")+(" + height + ")(" + base + ")+(" + height + ")(" + q_1 + ")"
T7: "w=" + q_1
T14: "y=" + base
T15: "z=" + height
T13: "x=" + height_1