Find Area of Rectilinear Figures

Students will find the area of L-shapes and other rectilinear figures (made of right angles) by decomposing them into two or more non-overlapping rectangles, finding the area of each, and adding the areas together.

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Grade 3 · Area and Multiplication · question 1 of 3

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12 rungs. A star at the top.

Uri measures shapes to cut fabric patches. Shape C is an L, so he finds each rectangle's area and adds them. What is its total area?

Your answer:

How it is taught

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Area is the flat space inside a shape.

For a rectangle, multiply the side lengths.

Read it: Cut it, then add the parts

A 3 by 5 rectangle. Cut 5 into 3 + 2. 3 × 3 = 9 and 3 × 2 = 6, so 9 + 6 = 15.

Cut the shape into rectangles along a line.
Find the area of each part.
Add the parts: 9 + 6 = 15.

Cutting does not add or take away a square, so the parts make the whole.

3 × 5 is the same as 3 × 3 and 3 × 2 put together.

An L-shape is 2 rectangles too, so cut it and add the parts.

To find an area, cut the shape into rectangles and add their areas.

Adding the side lengths, 3 + 5, instead of the squares.

Area counts the squares inside: 3 × 5 = 15, not 3 + 5.

An L-shape cuts into a 5 by 2 rectangle and a 2 by 3 rectangle. What is its area? — 16. 5 × 2 = 10 and 2 × 3 = 6; 10 + 6 = 16.

L-shape: 6×4 rectangle + 3×2 rectangle

Some shapes aren't simple rectangles. Look at this L-shape — how do we find its area?

Here's the trick: we can split it into two rectangles and add their areas.

Let's draw a line to break the L into a tall rectangle and a short rectangle.

Rectangle A is six units tall and four units wide.

Six times four is twenty-four square units.

Rectangle B is two units tall and three units wide.

Grade 3 · Break L-shapes into rectangles, then add

Two times three is six square units.

Now we add the two areas together: twenty-four plus six.

The total area is thirty square units. Great job breaking it apart!

Now you try. Find the area of this shape. What is its 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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