6th Grade Nets and Surface Area Worksheet Solutions (PDF)

6th Grade math worksheet solutions: Nets and Surface Area – Maths PDF

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This nets surface area answers for 6th Grade covers nets and surface area (Common Core 6.G.A.4), with a free PDF to print.

Check each surface area here. The solutions list every face, show each area, add them, and give the answer in square units in bold. Nets are included for many problems so you can see the faces.

Grade 6 · Common Core State Standards: 6.G.A.4

Nets surface area answers: exercises 1 to 10

Exercise 1 – Name the solid

Six rectangles in matching pairs fold into a box.

A rectangular prism

Exercise 2 – Surface area from a net

Faces: two \(5 \cdot 3 = 15\), two \(5 \cdot 4 = 20\), two \(3 \cdot 4 = 12\).

\(2(15 + 20 + 12) = 2 \cdot 47 = 94\)

\(94\text{ cm}^{2}\)

Exercise 3 – Surface area of a cube

A cube has 6 identical square faces. One face: \(6 \cdot 6 = 36\).

\(6 \cdot 36 = 216\)

\(216\text{ in}^{2}\)

Exercise 4 – Surface area of a prism

\(2(8 \cdot 2 + 8 \cdot 3 + 2 \cdot 3) = 2(16 + 24 + 6) = 2 \cdot 46 = 92\)

\(92\text{ ft}^{2}\)

Exercise 5 – Lateral area

Each side face is \(4 \cdot 9 = 36\).

\(4 \cdot 36 = 144\)

\(144\text{ in}^{2}\)

Exercise 6 – Square pyramid

Base: \(6 \cdot 6 = 36\). Each triangle: \(\frac{1}{2} \cdot 6 \cdot 5 = 15\).

\(36 + 4 \cdot 15 = 96\)

\(96\text{ cm}^{2}\)

Exercise 7 – Triangular prism

Two triangles: \(2 \cdot \frac{1}{2} \cdot 3 \cdot 4 = 12\).

Three rectangles: \(3 \cdot 10 + 4 \cdot 10 + 5 \cdot 10 = 120\).

\(12 + 120 = 132\)

\(132\text{ cm}^{2}\)

Exercise 8 – Find the edge of a cube

One face: \(150 \div 6 = 25\).

\(s^{2} = 25\), so \(s = 5\).

5 inches

Exercise 9 – Large pyramid

Base: 100. Each triangle: \(\frac{1}{2} \cdot 10 \cdot 13 = 65\).

\(100 + 4 \cdot 65 = 360\)

\(360\text{ m}^{2}\)

Four triangles around a square.

Exercise 10 – Wrapping paper

\(2(12 \cdot 8 + 12 \cdot 5 + 8 \cdot 5) = 2(96 + 60 + 40) = 392\)

\(392\text{ in}^{2}\)

Exercises 11 and up

Exercise 11 – Open-top tank

Bottom: \(20 \cdot 10 = 200\). Two long sides: \(2 \cdot 20 \cdot 12 = 480\). Two short sides: \(2 \cdot 10 \cdot 12 = 240\).

\(200 + 480 + 240 = 920\)

\(920\text{ in}^{2}\)

Exercise 12 – Does the net fold?

The center square plus 4 attached squares gives 5 faces. The sixth face is missing.

5 squares: it makes an open box (a cube with no top), not a closed cube.

Exercise 13 – Missing face

Full box: \(2(24 + 18 + 12) = 108\). Lid: \(6 \cdot 4 = 24\).

\(108 – 24 = 84\)

\(84\text{ in}^{2}\)

The five faces total 84.

Exercise 14 – Tent

Triangles: \(2 \cdot \frac{1}{2} \cdot 6 \cdot 8 = 48\).

Rectangles: \((6 + 8 + 10) \cdot 12 = 288\).

\(48 + 288 = 336\)

\(336\text{ ft}^{2}\)

Exercise 15 – Cereal box

\(2(7.5 \cdot 2 + 7.5 \cdot 10 + 2 \cdot 10) = 2(15 + 75 + 20) = 2 \cdot 110 = 220\)

\(220\text{ in}^{2}\)

Exercise 16 – Pyramid tent

Base: 64. Each triangle: \(\frac{1}{2} \cdot 8 \cdot 7 = 28\).

\(64 + 4 \cdot 28 = 176\)

\(176\text{ ft}^{2}\)

Exercise 17 – Cube or prism?

Cube: \(6 \cdot 25 = 150\).

Prism: \(2(20 + 24 + 30) = 148\).

The cube has the greater surface area (150 vs 148 square centimeters).

Exercise 18 – Decimal edges

\(2(2.5 \cdot 4 + 2.5 \cdot 6 + 4 \cdot 6) = 2(10 + 15 + 24) = 98\)

\(98\text{ m}^{2}\)

Exercise 19 – Painting a cube

\(6 \cdot 4 \cdot 4 = 96\) square feet.

\(96 \div 40 = 2.4\), so she needs 3 quarts.

\(96\text{ ft}^{2}\); 3 quarts

Six faces of 16 square feet.

Exercise 20 – Isosceles triangular prism

Triangles: \(2 \cdot \frac{1}{2} \cdot 6 \cdot 4 = 24\).

Rectangles: \((5 + 5 + 6) \cdot 9 = 144\).

\(24 + 144 = 168\)

\(168\text{ in}^{2}\)

Key facts behind this nets surface area answers

Key facts

A net shows all faces of a solid laid flat.
Surface area is the total area of all faces, in square units.
Rectangular prism: SA = 2(lw + lh + wh).
Pyramid: base area plus the areas of the triangular faces.
Triangular prism: two triangles plus three rectangles.

How to use this nets surface area answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

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