Back to Represent three-dimensional figures using nets

Represent Three-Dimensional Figures Using Nets

Show all work. For surface area, list each face and its area before summing. Include square units in all answers.

Grade 6·21 problems·~40 min·Common Core Math - Grade 6·standard·6-g-a-4

Work through problems with immediate feedback

Recall / Warm-Up

How many faces does a rectangular prism have?

What is the area of a rectangle with length 7 cm and width 3 cm?

10 cm²

20 cm²

21 cm²

42 cm²

A right triangle has legs of 5 in and 12 in. What is the area of the triangle in in²?

Fluency Practice

$Net of a rectangular prism showing six rectangles arranged in a cross pattern, with the six faces color-coded.$

How many rectangular faces does a valid net of a rectangular prism contain?

A triangular prism has how many faces total (including both triangular bases and all rectangular lateral faces)?

$Net of a rectangular prism with dimensions l=6 cm, w=4 cm, h=3 cm. Each of the six faces is labeled with its dimensions.$

A rectangular prism has $l = 6$ cm, $w = 4$ cm, $h = 3$ cm. Using the net, find the total surface area in cm².

A rectangular prism has $l = 5$ m, $w = 2$ m, $h = 8$ m. Find the total surface area in m².

A triangular prism has a right-triangle base with legs 3 ft and 4 ft (hypotenuse 5 ft), and a prism length of 10 ft. Find the total surface area in ft².

Varied Practice

A flat shape has exactly 6 rectangles arranged so that when folded, each rectangle becomes one face of a closed box. What 3D shape does it form?

Triangular prism

Square pyramid

Rectangular prism (box)

Triangular pyramid

$Two arrangements of 6 squares, one in a cross shape and one in a 2 by 3 grid, for students to compare as possible cube nets.$

Which statement about a net is correct?

Any arrangement of 6 squares is a valid net for a cube.

A valid net folds to cover all 6 faces without overlap or gaps.

A net must always be in a cross (plus-sign) shape.

The net of a cube has 4 squares.

A rectangular prism has $l = 4$ ft, $w = 3$ ft, $h = 2$ ft.
Top and bottom pair area: $2 \times (4 \times 3) =$ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ft²
Front and back pair area: $2 \times (4 \times 2) =$ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ft²
Left and right pair area: $2 \times (3 \times 2) =$ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ft²
Total surface area: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ft²

top/bottom area:

front/back area:

left/right area:

total SA:

$Net of a triangular prism with two isosceles triangle bases (base 6 in, height 4 in) and three rectangles (each 6 in by 8 in).$

A triangular prism has an isosceles-triangle base with base 6 in and height 4 in. Each of the three equal rectangular faces is 6 in × 8 in. Find the total surface area in in².

Word Problems

Kenji is wrapping a rectangular gift box with dimensions 10 in × 6 in × 3 in.

How many square inches of wrapping paper are needed to cover all 6 faces of the box?

A roll of wrapping paper is 200 in² per sheet. How many sheets does Kenji need?

1 sheet

2 sheets

3 sheets

4 sheets

A storage shed is a rectangular prism (12 ft × 8 ft × 9 ft) with no floor; only the walls and roof need to be painted.

Complete the reasoning.
Full surface area = ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ft²
Floor area = ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ft²
Area to be painted = ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ft²

full surface area:

floor area:

painted area:

A tent is a triangular prism with triangular ends (base 4 m, height 3 m), two slanted rectangular sides (5 m × 6 m each), and a floor (4 m × 6 m); only the two slanted sides and two triangular ends need a tarp.

What is the area of the tarp needed in m²?

A company makes cardboard boxes (rectangular prisms) with $l = 8$ in, $w = 5$ in, $h = 4$ in. Cardboard costs $0.02 per square inch.

Complete the reasoning.
Surface area = ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ in²
Cost of cardboard = ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲

surface area:

cost:

Error Analysis

Anika finds the surface area of a rectangular prism with $l = 5$ cm, $w = 3$ cm, $h = 4$ cm. She writes:
Front: $5 \times 4 = 20$ cm²
Top: $5 \times 3 = 15$ cm²
Right side: $3 \times 4 = 12$ cm²
Total SA $= 20 + 15 + 12 = 47$ cm²

What error did Anika make? What is the correct surface area?

Anika used the wrong formula. She should have used $SA = lwh$ .

Anika only counted 3 of the 6 faces. Each face has an opposite congruent face. Correct SA $= 2(20) + 2(15) + 2(12) = 94$ cm².

Anika's answer is correct.

Anika should have added the dimensions: $5 + 3 + 4 = 12$ cm².

Tariq needs the surface area of a box with $l = 6$ ft, $w = 2$ ft, $h = 4$ ft. He computes:
$V = 6 \times 2 \times 4 = 48$ ft³ and reports "The surface area is 48 ft³."

What two errors did Tariq make?

Tariq computed volume ( $V = lwh$ ), not surface area. Also, surface area uses square units (ft²), not cubic units (ft³).

Tariq computed the correct answer; 48 ft² is the surface area.

Tariq should have divided by 2 to get the surface area.

Tariq's formula is correct, but he used the wrong dimensions.

Challenge / Extension

A square pyramid has a square base of side 6 cm. Each of the four triangular lateral faces has a base of 6 cm and a slant height of 5 cm (the height of each triangular face, measured along the slant). What is the total surface area of the pyramid in cm²?

Two rectangular prisms have the same volume. Prism A has dimensions 4 cm × 4 cm × 4 cm. Prism B has dimensions 8 cm × 8 cm × 1 cm. Do they have the same surface area? Show your work and explain what this tells you about the relationship between volume and surface area.

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