Surface Area Using Nets · MCAP 6.G.A.4

Learning Goal: Use nets to find the surface area of prisms and pyramids by finding the area of every face and adding them.

Vocabulary

netA flat (2D) pattern that folds up to make a 3D solid; it shows every face laid out flat.

surface areaThe total area of all the faces (outside surfaces) of a 3D solid, in square units.

faceOne of the flat surfaces of a 3D solid, such as one side of a box.

slant heightOn a pyramid, the height of a triangular face measured from the base edge to the top point.

What You Need to Know

Surface area = the sum of the areas of all the faces. A net helps you see and count every face.
A rectangular prism has 6 faces in 3 matching pairs: surface area = 2(lw + lh + wh).
A cube has 6 equal square faces: surface area = 6 × (edge × edge).
A triangular prism has 2 triangle faces plus 3 rectangle faces; add all 5 areas.
A square pyramid has 1 square base plus 4 triangles: area = base + 4 × (1/2 × base edge × slant height).
Surface area is always written in square units, such as cm², in², or m².

Worked Example I Do — watch how it works

A rectangular prism (box) is 5 cm long, 3 cm wide, and 4 cm tall. Find its surface area.

Step 1. Find the three different face areas: lw = 15, lh = 20, wh = 12.
Step 2. Each face has a matching pair, so add them: 15 + 20 + 12 = 47.
Step 3. Surface area = 2 × 47 = 94 cm².

Answer: 94 cm²

Guided Practice We Do — try it together

1. A cube has edges of 7 in. Find its surface area.
💡 Hint: All 6 faces are equal squares: 6 × (7 × 7).
2. A square pyramid has a base 6 m on each side and a slant height of 5 m. Find the surface area.
💡 Hint: Base area = 6 × 6. Each triangle = 1/2 × 6 × 5; there are 4 of them.
3. A triangular prism has two triangular faces, each with a base of 6 ft and a height of 4 ft. Find the combined area of just the two triangle faces.
💡 Hint: One triangle = 1/2 × 6 × 4; you need two of them.

Independent Practice You Do — show your work

1. A rectangular prism is 6 cm by 2 cm by 3 cm. Find its surface area.
2. A cube has edges of 5 in. Find its surface area.
3. A square pyramid has a base 8 m on each side and a slant height of 6 m. Find its surface area.
4. A rectangular prism is 10 in by 4 in by 4 in. Find its surface area.
5. A box is 2 cm by 2 cm by 9 cm. Find its surface area.

MCAP-Style Practice

Directions: Answer each item the way you would on the MCAP. For selected-response items, fill in the circle (○) next to the correct answer. For constructed-response items, enter your answer and show your work. Every item below assesses standard 6.G.A.4.

Item 1Selected Response6.G.A.4

A cube has edges of 4 cm. What is its surface area?

Select the correct answer.

○ A. 16 cm²○ B. 64 cm²○ C. 96 cm²○ D. 384 cm²

Item 2Selected Response6.G.A.4

A rectangular prism is 5 in long, 2 in wide, and 3 in tall. What is its surface area?

Select the correct answer.

○ A. 30 in²○ B. 31 in²○ C. 47 in²○ D. 62 in²

Item 3Constructed Response6.G.A.4

A square pyramid has a base 10 ft on each side and a slant height of 4 ft. Find the total surface area.

Enter your answer in the space provided. Show your work.

Enter your answer:

Teacher Answer Key (click to show)

Independent 1	72 cm²
Independent 2	150 in²
Independent 3	160 m²
Independent 4	192 in²
Independent 5	80 cm²
Item 1 · 6.G.A.4	C — A cube has 6 equal faces: 6 × (4 × 4) = 6 × 16 = 96 cm².
Item 2 · 6.G.A.4	D — Surface area = 2(lw + lh + wh) = 2(10 + 15 + 6) = 2 × 31 = 62 in².
Item 3 · 6.G.A.4	180 ft² — Base = 100 ft²; four triangles = 4 × (1/2 × 10 × 4) = 80 ft²; total = 180 ft².

Neft Teacher · Grade 6 MCAP Mathematics Review · Standard 6.G.A.4