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Find Area and Surface Area of 2D and 3D Figures

Students find the area of triangles, quadrilaterals, and composite 2D figures. They also find the surface area of prisms, pyramids, and composite 3D solids by decomposing them into flat faces and summing the areas.

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Find Area and Surface Area of 2D and 3D Figures

Grade 7 · Geometry · question 1 of 3

0 of 20

20 rungs. A star at the top.

A = (5 × 2) ÷ 2 =

How it is taught

0:00 of 4:19

Surface area is the total area of all the faces.

A rectangular prism has 6 rectangular faces.

Matching faces come in pairs.

Read it: Surface area from a net

A 5 by 3 by 2 box unfolds into 6 rectangles in 3 matching pairs: two of 5 × 3 = 15, two of 5 × 2 = 10 and two of 3 × 2 = 6. One of each pair is 15 + 10 + 6 = 31, so the surface area is 2 × 31 = 62 square units.

  1. Unfold the box: each face is one rectangle in the net.
  2. Find one rectangle of each matching pair, and add them.
  3. Double it, because every pair has 2 faces.

Top and bottom, front and back, and the two ends match, so 3 areas cover all 6 faces.

A cube's 6 faces are all the same square, so its surface area is 6 times one square.

Surface area covers the outside, so it adds the faces; volume fills the inside, so it multiplies the edges.

Surface area = 2 × (length × width + length × height + width × height).

Working out the volume instead: 5 × 3 × 2 = 30.

Surface area adds the faces: 2 × (15 + 10 + 6) = 62.

Each square of a cube's net is 12 by 12. Its surface area is ___ square units. — 864. Each square is 12 × 12 = 144, and 6 × 144 = 864.

5 × 3 × 2 box

Imagine wrapping this box. How much paper do we need? That's called surface area.

Grade 7 · Adding the areas of all six faces

This box is five units long, three units wide, and two units tall.

A box has six flat faces — three matching pairs.

The top and bottom are both five-by-three rectangles. Each one has area fifteen.

Two of them, so that's thirty square units in all.

The front and back are both five-by-two. Each one has area ten.

Two of them gives us twenty.

The left and right sides are both three-by-two. Each one has area six.

Two of those is twelve.

Now we add them up: thirty plus twenty plus twelve.

Sixty-two square units. That's the surface area of our box!

Now you try. Find the surface area of this box. What is the surface area?

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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