Lesson 2 of 5

Area.

About 25 minutes · 6 practice questions

Area counts squares: a rectangle, then a parallelogram, a triangle and a trapezoid cut and rearranged, and a circle unrolled into a strip.

Step 1 of 6 · Counting squares

Step 1 of 6

Counting squares

Area is how much surface a shape covers. It is measured in squares: a square with side $1$ ⁠ is one unit of area. In a rectangle the squares sit in equal rows, so there is no need to count them one by one: there are as many rows as the height, and as many squares in each row as the base. Move Base and Height, and drag Look inside to fill the rectangle row by row.

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Step 2 of 6

Perimeter and area

The perimeter is something else: the length of the line around the shape, like a fence round a garden. Area counts the squares inside; the perimeter counts steps along the edge. The two numbers can be close, but they measure different things.

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Step 3 of 6

A parallelogram

A parallelogram has two pairs of parallel sides and leans to one side. The dashed line is its height: the distance at right angles from the bottom base to the top side. Predict its area, then see what happens when one piece is cut off and moved.

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Step 4 of 6

A triangle

Every triangle is half a parallelogram: turn a copy of it half a turn about the middle of one side, and the two complete each other. Answer, then drag Look inside to watch the copy turn.

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Step 5 of 6

A trapezoid

A trapezoid has two parallel bases of different lengths. The same idea works here: an upside-down copy completes it to a parallelogram, whose base is the two bases together.

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Step 6 of 6

A circle

A circle has no straight sides, but you can cut it into slices like a cake and lay them alternately. The thinner the slices, the closer the shape comes to a rectangle whose height is the radius $r$ ⁠ and whose width is half the circumference. The circumference of a circle is $2\pi r$ ⁠, where $\pi \approx 3.14$ ⁠, so the width is $\pi r$ ⁠ and the area $\pi r \times r = \pi r^2$ ⁠.

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Interactive scene

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Each step sets up the Scene for you, and a control marked “fixed” stays put for that step.

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Practice · Reach the target

Set Base and Height so that the rectangle covers exactly $24$ ⁠ squares, then press Check.

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Practice · Calculate

The rectangle’s base is $7$ ⁠ and its height $3$ ⁠. What is its perimeter, the length of the line around it?

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Practice · Predict, then look

The parallelogram has base $6$ ⁠ and height $4$ ⁠. Its slanted side is longer than the height, about $4.47$ ⁠. What is its area?

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Practice · Calculate

The triangle has base $8$ ⁠ and height $5$ ⁠. What is its area?

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Practice · Calculate

The trapezoid has two parallel bases, $8$ ⁠ at the bottom and $4$ ⁠ at the top, and the height between them is $3$ ⁠. What is its area?

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Practice · Calculate

The circle’s radius is $3$ ⁠. What is its area? Round to two decimal places.