Area & Perimeter Explorer

Pick a shape, drag the sliders, and watch the area and perimeter update in real time. Every answer includes the formula and a step-by-step calculation. All computation runs in your browser.

Shape

Dimensions

Width (w)8

Height (h)5

Show grid background

Try an example

Area

40

square units

Perimeter

26

units

Area Calculation

A = w \times h

A = 8 \times 5

A = 40

Perimeter Calculation

P = 2(w + h)

P = 2(8 + 5)

P = 2 \times 13

P = 26

Reference Guide

Rectangle and Square

A rectangle has four right angles. A square is a special rectangle where all sides are equal.

A = w \times h

P = 2(w + h)

For a square with side $s$ , the area simplifies to $s^2$ and the perimeter to $4s$ .

Triangle

The area of a triangle is half the product of its base and height. The height must be perpendicular to the base.

A = \frac{1}{2} \times b \times h

The perimeter is the sum of all three sides. For a right triangle with legs $a$ and $b$ , the hypotenuse is $c = \sqrt{a^2 + b^2}$ .

Parallelogram and Trapezoid

A parallelogram has two pairs of parallel sides. Its area formula is the same as a rectangle using the perpendicular height, not the slant side.

A_{\text{parallelogram}} = b \times h

A trapezoid has one pair of parallel sides. Its area uses the average of the two bases.

A_{\text{trapezoid}} = \frac{1}{2}(b_1 + b_2) \times h

Circle

A circle is defined by its radius $r$ . Its perimeter is called the circumference.

A = \pi r^2

C = 2\pi r

The constant $\pi \approx 3.14159$ is the ratio of every circle's circumference to its diameter. You can also write the circumference as $C = \pi d$ where $d = 2r$ .