A quadrilateral is formed by the points (0,0) and (5,10) and (10,15) and (5,5)
Calculate the perimeter and area of ABCD and determine if it is a parallelogram
Calculate the distance AB between (0,0) and (5,10)
AB = Square Root((x2 - x1)2 + (y2 - y1)2)
AB = Square Root((5 - 0)2 + (10 - 0)2)
AB = Square
Root((52 + 102))
AB = √(25 + 100)
AB = √125
AB = 11.180339887499
Calculate the distance BC between (5,10) and (10,15)
BC = Square Root((x2 - x1)2 + (y2 - y1)2)
BC = Square Root((10 - 5)2 + (15 - 10)2)
BC = Square Root((52 +
52))
BC = √(25 + 25)
BC = √50
BC = 7.0710678118655
Calculate the distance CD between (10,15) and (5,5)
CD = Square Root((x2 - x1)2 + (y2 - y1)2)
CD = Square Root((5 - 10)2 + (5 - 15)2)
CD = Square Root((-52 + -102))
CD = √(25
+ 100)
CD = √125
CD = 11.180339887499
Calculate the distance AD between (0,0) and (5,5)
AD = Square Root((x2 - x1)2 + (y2 - y1)2)
AD = Square Root((5 - 0)2 + (5 - 0)2)
AD = Square Root((52 + 52))
AD = √(25 + 25)
AD =
√50
AD = 7.0710678118655
Calculate the perimeter of ABCD
Perimeter of ABCD = AB + BC + CD + AD
Perimeter of ABCD = 11.180339887499 + 7.0710678118655 + 11.180339887499 + 7.0710678118655
Perimeter of ABCD = 36.502815398729
Calculate the semi-perimeter (s) of ABCD
s = 18.251407699364
Calculate the Area (A) using Brahmagupta's Formula
A = √(s - a)(s
- b)(s - c)(s - d)
A = √(18.251407699364 - 11.180339887499)(18.251407699364 - 7.0710678118655)(18.251407699364 - 11.180339887499)(18.251407699364 - 7.0710678118655)
A = √(7.0710678118655)(11.180339887499)(7.0710678118655)(11.180339887499)
A = √(6250
A = 79.056941504209
How does the Quadrilateral Calculator work?
Given 4 points entered, this determines the area using Brahmaguptas Formula and perimeter of the quadrilateral formed by the points as well as checking to see if the quadrilateral (quadrangle) is a parallelogram.
What formulas are used for Quadrilateral?
Perimeter of ABCD = AB + BC + CD +AD
s = ½P
A = √(s - a)(s - b)(s - c)(s - d)
What 3 concepts are covered in the Quadrilateral Calculator?
parallelogramperimeterThe distance around a shape or objectquadrilateralPolygon with 4 edges/sides and 4 corners/vertices
Quadrilateral Calculator Video
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Created by Hanna Pamuła, PhD candidate
Reviewed by Bogna Szyk and Steven Wooding
Last updated: Sep 14, 2022
If you have any problems with the geometry of a parallelogram, check this parallelogram area calculator (and also its twin brother, parallelogram perimeter calculator).
Whether you want to calculate the area given base and height, sides and angle, or diagonals of a parallelogram and angle between them, you are in the right place. Don't ask how to find the area of a parallelogram; just give the calculator a try!
Below you can find out how the tool works – the parallelogram area formulas and neat explanation are all you need to understand the topic.
Parallelogram area formulas
A parallelogram is a simple quadrilateral with two pairs of parallel sides. Every rectangle is a parallelogram, as well as every rhombus and square. Remember, it doesn't work the other way around!
Which formulas does the parallelogram area calculator use?
Area given base and height
area = base × height
Did you notice something? The formula for the area of a parallelogram is pretty much the same as for a rectangle! Why is it so? Have a look at the picture: a parallelogram can be divided into a trapezoid and a right triangle and rearranged to the rectangle.
Learn more about rectangle area with our area of a rectangle calculator.
Area given sides and the angle between them
area = a × b × sin(angle)
Does it ring a bell? This formula comes from trigonometry and is used, for example, in our triangle area calculator – the parallelogram may be seen as two congruent triangles. The adjacent angles in the parallelogram are supplementary, so you can choose whichever angle you want because sin(angle) = sin(180° - angle).
Area given diagonals of a parallelogram and the angle between them
area = ½ × e × f × sin(angle)
The formula comes from trigonometry as well. Do you want to know where it comes from?
Divide the parallelogram into two triangles, and assume that our e diagonal is the "base" for both new triangles.
What's the height of that triangle? Use the sine function. It's (f/2) × sin(angle)!
The area of the triangle is equal to our "base" e times height: e × (f/2) × sin(angle)
The parallelogram consists of two such triangles, so the area equals e × f × sin(angle).
How to use this parallelogram area calculator?
Are you still not sure our parallelogram area calculator works? We will show you step by step:
Have a look at your exercise. What is given, what is unknown? Choose the right calculator part for your needs. Assume that we want to calculate the area knowing the diagonals of a parallelogram and the angle between diagonals.
Enter the given values to the right boxes. Assume 5 in, 13 in, and 30° for the first diagonal, the second one, and the angle between them, respectively.
The calculator displays the area of a parallelogram value. It's 32.5 in² in our case.
Check out our area calculators for other shapes, such as rhombus area calculator, circle area calculator, and trapezoid area calculator.
FAQ
How do I find the area of a parallelogram given its adjacent sides?
To determine the area given the adjacent sides of a parallelogram, you also need to know the angle between the sides. Then you can apply the formula: area = a × b × sin(α), where a and b are the sides, and α is the angle between them.
How do I find the area of a parallelogram given diagonals?
The area of a parallelogram can be determined from its diagonals, provided that you also know the angle between the diagonals.
If e and f are the lengths of the diagonals and φ is the angle between them, then the area can be calculated as follows: area = ½ × e × f × sin(φ).
How do I find the area of a parallelogram without height?
It is possible to find the area of a parallelogram without height! For instance, it suffices to know one of the following things:
- The length of adjacent sides and the angle between them – use trigonometry.
- The length of diagonals and the angle between them, using the formula – use trigonometry.
- The length of diagonals and one side – use Heron's formula.
What is the area of a parallelogram with perpendicular diagonals of length 10 and 15?
The answer is 75. We use the formula that says the area is equal to ½ times the product of the lengths of the diagonals times the sine of the angle between them. As our diagonals are perpendicular, the angle between them is 90° and sin 90° = 1. Hence, the calculation we need to perform is ½ × 10 × 15 = 75.
Hanna Pamuła, PhD candidate
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