Area is the amount of surface a flat shape covers, measured in square units. It counts how many unit squares fit inside the shape, which is why the units are squared. A rectangle’s area is length times width, so a 5 by 3 rectangle has area 15 square units.
Area counts the unit squares that cover a shape. A rectangle’s squares come in rows, so you multiply; a triangle covers exactly half of the matching rectangle.
Formal definition and notation
Area measures the amount of flat space inside a two-dimensional shape. A unit square, a square with sides of 1 unit, has an area of 1 square unit, and the area of any plane figure is the number of unit squares (including parts of squares) needed to cover it with no gaps or overlaps. Area is written in square units such as cm2, in2 or ft2.
Symbol
Read it as
Meaning
A
A
the usual letter for area in formulas
cm2
square centimeters
the area of squares 1 cm on each side; the little 2 means two dimensions are multiplied
Area and perimeter are different: perimeter is the distance around a shape, area is the space inside it.
A triangle is half of a rectangle (or parallelogram) with the same base and height, which is where the 12 comes from.
For an L-shape or other composite figure, split it into rectangles and triangles and add their areas, or subtract a missing piece.
When every length doubles, the area becomes 4 times as large, because both dimensions double.
Area formulas
Area formulas
rectangle A = l × w; triangle A = 12 × b × h
l, w
the length and the width of the rectangle, in the same unit
b
the base of the triangle: any side you choose
h
the height: the perpendicular distance from the base to the opposite corner
Other shapes: square A = s2, parallelogram A = b × h, circle A = π r2. Multiply two lengths in the same unit, and the answer is in square units.
Try it: count the squares
Interactive
Drag the corner handle or use the steppers to change the length and width. The grid shows every unit square, and the readout compares the area with the perimeter.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Area examples, step by step
Example 1: Area of a square
Warm-up
A square tile is 7 inches on each side. What is its area?
A square is a rectangle whose length and width are equal, both 7 inches.
Multiply: A = 7 × 7 = 49.
The units are inches times inches, so the area is in square inches.
Answer: The area is 49 square inches.
Example 2: Area of a triangle
Core
A triangle has a base of 10 cm and a height of 6 cm. Find its area.
Perimeter is the distance around a shape, in units; area is the space inside, in square units. A 5 by 3 rectangle has perimeter 16 units and area 15 square units.
Volume counts unit cubes that fill a solid, in cubic units. Area counts unit squares that cover a flat shape.
Quick check: 3 questions
Question 1 of 3
What is the area of a rectangle that is 9 units long and 4 units wide?
Show answer and explanation
Answer: C.9 × 4 = 36, and area is in square units. Choice A is the perimeter, choice B adds two sides, and choice D has the right number but a length unit.
Question 2 of 3
A triangle has base 8 cm and height 5 cm. What is its area?
Show answer and explanation
Answer: B.12 × 8 × 5 = 20. Choice A forgets the 12, choice C adds the base and height, and choice D halves twice.
Question 3 of 3
A square has an area of 9 square inches. If you double the length of each side, what is the new area?
Show answer and explanation
Answer: D. The side is 3 inches, so the new side is 6 inches and the new area is 6 × 6 = 36. Doubling both dimensions multiplies the area by 4, not 2 (choice A).
Area: frequently asked questions
Why is area measured in square units?
Because area counts how many unit squares cover a shape. A square 1 inch on each side covers 1 square inch, so a rectangle that holds 15 of those squares has an area of 15 square inches. Multiplying inches by inches also gives in2, the same idea written with an exponent.
What is the difference between area and perimeter?
Perimeter is the distance around the outside of a shape, so it is a length, such as 16 feet. Area is the amount of surface inside, so it is in square units, such as 15 square feet. Fencing a yard uses perimeter; buying grass seed or carpet uses area. Two shapes can share a perimeter and have different areas.
How do you find the area of an irregular shape?
Break it into simple pieces such as rectangles and triangles, find each area, and add them. Sometimes it is easier to find a big rectangle and subtract the missing corner. On a grid, you can also count whole squares and match up half squares to estimate.
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