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Rectangle Calculator

Rectangle calculator

The rectangle solver finds missing width, length, diagonal, area or perimeter of a rectangle. The calculator accepts all types of input values, including fractions and square roots, and provides step-by-step explanation.

Input two elements of a rectangle and select element to find.
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Solve for

0123456789/.√C ✖

Input any two elements of a rectangle.

side

a =

side

b =

diagonal

d =

area

A =

perimeter

P =

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Rectangle formulas

A = ab

area

P = 2 a + 2 b

perimeter

d^{2} = a^{2} + b^{2}

diagonal

Examples

ex 1:

Find the area of the rectangle whose sides are a=5/3 cm and b=3/2cm.

ex 2:

If the diagonal is 9cm and one side is 5cm, find the area of a rectangle.

ex 3:

A rectangle has an area of 18 cm² and a side length of 16/5cm. Determine the perimeter.

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TUTORIAL

Rectangle calculations

This calculator uses the following formulas to find the missing values of a rectangle:

Area:	$A = a \cdot b$
Perimeter:	$P = 2 a + 2 b$
Diagonal:	$d^{2} = a^{2} + b^{2}$

Example 01 :

What is the area of a rectangle with a base of 12 cm and a height of 3/2 cm?

Solution:

base $a = 6$

height $b = \frac{9}{2}$

A = a \cdot b = 6 \cdot \frac{9}{2} = \frac{54}{2} = 27

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Example 02 :

What is the perimeter of a rectangle with a length of 7/2cm and a width of 5/2cm?

Solution:

length $a = \frac{7}{2} c m$

width $b = \frac{5}{2} c m$

P = 2 a + 2 b = 2 \cdot \frac{7}{2} + 2 \cdot \frac{5}{2} = 7 + 5 = 12

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Example 03 :

The area of a rectangle is 42 cm². Find its perimeter if the width is 7cm.

Solution:

We'll need two steps to solve this one:

Step 1: find length ( b ):

width $a = 7 c m$

area: $A = 42 c m$

A 42 b b = a \cdot b = 7 \cdot b = \frac{42}{7} = 6

Step 2: find perimeter ( P )

width $a = 7 c m$

length $b = 6 c m$

P P P P = 2 a + 2 b = 2 \cdot 7 + 2 \cdot 6 = 14 + 12 = 28 c m^{2}

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Example 04 :

What is the diagonal of a rectangle if the perimeter is P = 11/2 cm and a width is a = 3/2 cm ?

Solution:

Step 1: find length ( b ):

width $a = \frac{3}{2} c m$

perimeter: $P = \frac{11}{2} c m$

P \frac{11}{2} \frac{11}{2} 2 b 2 b b = 2 a + 2 b = 2 \cdot \frac{3}{2} + 2 b = 3 + 2 b = \frac{11}{2} - 3 = \frac{5}{2} = \frac{5}{4}

Step 2: find diagonal ( d )

width $a = \frac{3}{2} c m$

length $b = \frac{5}{4} c m$

d^{2} d^{2} d^{2} d^{2} d = a^{2} + b^{2} = (\frac{3}{2})^{2} + (\frac{5}{4})^{2} = \frac{9}{4} + \frac{25}{16} = \frac{61}{16} = \frac{61}{4}

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