Volume of Square Based Pyramid

G.13 Surface Area and Volume

Make sure you have your formulas handy!

Square Pyramid

a three-dimensional shape with a square base and four triangular faces that meet at a point called the apex

First we will find Surface Area(SA).

l is your slant height.

p is your perimeter of your square base (4 times the side length)

B is your Area of the base (side x side)

SA = 1/2lp + B

1/2 x 17 x 4(16) + 16²

1/2 x 17 x 64 + 256

SA = 800 inches²

Multiple Choice

Find the surface area of this square pyramid.

• 32 units²

• 80 units²

• 320 units²

• 640 units²

Multiple Choice

Find the surface area of this square pyramid.

• 1025 feet²

• 2050 feet²

• 2225 feet²

• 4450 feet²

Multiple Choice

Find the surface area of this pyramid with a square base.

• 360 units²

• 165 units²

• 720 units²

• 750 units²

Volume of a Square Pyramid

V = 1/3Bh

B=Area of the base (side²)

h = height of the pyramid (forms a right angle with base)

Find the volume of this square pyramid.

V = 1/3 B h

1/3 x 6² x 8

96 inches³

Multiple Choice

Find the volume of this square pyramid.

• 6144 units³

• 128 units³

• 3072 units³

• 2048 units³

Multiple Choice

Find the volume of this square pyramid.

• 2 cm³

• 4 cm³

• 6 cm³

• 12 cm³

Multiple Choice

Find the volume of this square pyramid.

• 1280 in³

• 1450.67 in³

• 1445 in³

• 1541.33 in³

Rectangular prism

A 3-dimensional (has length, width, and height) shape that has a rectangular base and 6 rectangular faces.

Surface Area of a rectangular prism

SA = 2lw + 2lh + 2wh l=11, w=5, h=6

2(11)(5) + 2(11)(6) + 2(5)(6)

302 cm²

Multiple Choice

Find the Surface Area of this Rectangular Prism.

• 18 feet²

• 144 feet²

• 36 feet²

• 72 feet²

Multiple Choice

Find the Surface Area of this rectangular prism.

• 100 cm²

• 56 cm²

• 50 cm²

• 200 cm²

Volume of a rectangular prism

V=lwh

l=11, w=5, h=6

11 x 5 x 6

330 cm³

Multiple Choice

Find the Volume of this Rectangular Prism.

• 18 feet³

• 144 feet³

• 36 feet³

• 72 feet³

Multiple Choice

Find the Volume of this rectangular prism.

• 100 cm³

• 56 cm³

• 50 cm³

• 200 cm³

A triangular prism has 2 congruent triangular bases and three rectangular faces.

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SA = hp + 2B

h = height of the prism (not on the triangle)=12

p = perimeter of base(add up the 3 sides) = 8+8+8

B = area of base (1/2bh) = 1/2 x 8 x 3

SA = hp + 2B

12(8 + 8 + 8) + 2(1/2 x 8 x 3)

312 cm²

Multiple Choice

Find the surface area of this triangular prism.

• 990 mm²

• 870 mm²

• 1190 mm²

• 2280 mm²

Multiple Choice

Find the surface area of this triangular prism.

• 1092 mm²

• 624 mm²

• 840 mm²

• 1248 mm²

Multiple Choice

Find the surface area of this triangular prism.

• 240 in²

• 90 in²

• 120 in²

• 180 in²

V = Bh

h = height of the prism (not one of the sides of the triangle)=12

B = area of base (1/2bh) = 1/2 x 8 x 3

V = Bh

(1/2 x 8 x 3) x 12

144 cm³

Multiple Choice

Find the volume of this triangular prism.

• 1092 mm³

• 624 mm³

• 840 mm³

• 1248 mm³

Multiple Choice

Find the volume of this triangular prism.

• 990 mm³

• 870 mm³

• 1190 mm³

• 2280 mm³

Multiple Choice

Find the volume of this triangular prism.

• 240 in³

• 90 in³

• 120 in³

• 180 in3