Area Formulas for 2D Shapes and Common Solids

Direct answer

What is an area formula?

Area formulas calculate the flat space inside a 2D shape or the base of a 3D solid. Common area formulas include square area $A = s^{2}$ , rectangle area $A = l w$ , triangle area $A = 1/2 bh$ , and circle area $A = π r^{2}$ .

Quick table

Area formulas table

Shape	Formula	Use
Square	$A = s^{2}$	s = side length
Rectangle	$A = l w$	l = length, w = width
Triangle	$A = \frac{1}{2} \times b \times h$	b = base, h = height
Circle	$A = π r^{2}$	r = radius
Parallelogram	$A = bh$	b = base, h = height
Trapezoid	$A = \frac{1}{2} (a + b) h$	a and b = parallel bases, h = height
Rhombus	$A = 1/2 d_{1} d_{2}$	d1 and d2 = diagonals
Cube face	$A = s^{2}$	Area of one square face
Cylinder base	$A = π r^{2}$	Area of the circular base

Formula cards

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Circle Formulas

Area $A = π r^{2}$

Circumference $C = 2 π r = π d$

Diameter $d = 2 r$

Radius $r = \frac{d}{2}$

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Triangle Formulas

Area $A = \frac{1}{2} bh$

Perimeter $P = a + b + c$

Right triangle $a^{2} + b^{2} = c^{2}$

Heron's formula $A = s (s - a) (s - b) (s - c)$

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Cylinder Formulas

Volume $V = π r^{2} h$

Lateral surface area $L S A = 2 π r h$

Total surface area $T S A = 2 π r (r + h)$

Base area $B = π r^{2}$

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Cone Formulas

Volume $V = \frac{1}{3} π r^{2} h$

Lateral surface area $L S A = π r l$

Total surface area $T S A = π r (r + l)$

Slant height $l = r^{2} + h^{2}$

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Sphere Formulas

Volume $V = \frac{4}{3} π r^{3}$

Surface area $S A = 4 π r^{2}$

Diameter $d = 2 r$

Radius $r = \frac{d}{2}$

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Examples

Step-by-step examples

Rectangle area

Given l = 12 cm and w = 4 cm.
Use $A = l w$ .
$A = 12 \times 4 = 48 c m^{2}$ .

Triangle area

Given b = 10 m and h = 7 m.
Use $A = 1/2 bh$ .
$A = \frac{1}{2} \times 10 \times 7 = 35 m^{2}$ .

Circle area

Given r = 3 in.
Use $A = π r^{2}$ .
$A = 9 π \approx 28.27 i n^{2}$ .

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FAQ

Area Formulas FAQ

What is the area formula for a rectangle?

The rectangle area formula is $A = l w$ , where l is length and w is width.

What is the area formula for a circle?

The circle area formula is $A = π r^{2}$ , where r is the radius.

Do area answers need square units?

Yes. Area is always written in square units, such as cm2 or square meters.