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## Area of Concave Quadrilateral Solution

STEP 0: Pre-Calculation Summary
Formula Used
area = sqrt(((Outer side a+Inner Diagonal+Inner side d)/2)*((Outer side a+Inner Diagonal+Inner side d)/(2-Outer side a))*((Outer side a+Inner Diagonal+Inner side d)/(2-Inner Diagonal))*((Outer side a+Inner Diagonal+Inner side d)/(2-Inner side d)))+ sqrt(((Outer side b+Inner Diagonal+Inner side c)/2)*((Side B+Diagonal+Side C)/(2-Side B))*((Outer side b+Inner Diagonal+Inner side c)/(2-Inner Diagonal))*((Outer side b+Inner Diagonal+Inner side c)/(2-Inner side c)))
A = sqrt(((a+f+d)/2)*((a+f+d)/(2-a))*((a+f+d)/(2-f))*((a+f+d)/(2-d)))+ sqrt(((b+f+c)/2)*((Sb+d+Sc)/(2-Sb))*((b+f+c)/(2-f))*((b+f+c)/(2-c)))
This formula uses 1 Functions, 8 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Outer side a - Outer side a is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back. (Measured in Meter)
Inner diagonal - Inner diagonal is a straight line joining two opposite corners of a square, rectangle, or another straight-sided shape. (Measured in Meter)
Inner side d - Inner side d is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back. (Measured in Meter)
Outer side b - Outer side b is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back. (Measured in Meter)
Inner side c - Inner side c is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back. (Measured in Meter)
Side B - Side B is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back. (Measured in Meter)
Diagonal - A diagonal is a straight line joining two opposite corners of a square, rectangle, or another straight-sided shape. (Measured in Meter)
Side C - Side C is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Outer side a: 4.8 Meter --> 4.8 Meter No Conversion Required
Inner diagonal: 1.922 Meter --> 1.922 Meter No Conversion Required
Inner side d: 3.478 Meter --> 3.478 Meter No Conversion Required
Outer side b: 4 Meter --> 4 Meter No Conversion Required
Inner side c: 2.3 Meter --> 2.3 Meter No Conversion Required
Side B: 7 Meter --> 7 Meter No Conversion Required
Diagonal: 8 Meter --> 8 Meter No Conversion Required
Side C: 4 Meter --> 4 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
A = sqrt(((a+f+d)/2)*((a+f+d)/(2-a))*((a+f+d)/(2-f))*((a+f+d)/(2-d)))+ sqrt(((b+f+c)/2)*((Sb+d+Sc)/(2-Sb))*((b+f+c)/(2-f))*((b+f+c)/(2-c))) --> sqrt(((4.8+1.922+3.478)/2)*((4.8+1.922+3.478)/(2-4.8))*((4.8+1.922+3.478)/(2-1.922))*((4.8+1.922+3.478)/(2-3.478)))+ sqrt(((4+1.922+2.3)/2)*((7+8+4)/(2-7))*((4+1.922+2.3)/(2-1.922))*((4+1.922+2.3)/(2-2.3)))
Evaluating ... ...
A = 341.925107796946
STEP 3: Convert Result to Output's Unit
341.925107796946 Square Meter --> No Conversion Required
341.925107796946 Square Meter <-- Area
(Calculation completed in 00.032 seconds)

## < 7 Concave Quadrilateral Calculators

Area of Concave Quadrilateral
area = sqrt(((Outer side a+Inner Diagonal+Inner side d)/2)*((Outer side a+Inner Diagonal+Inner side d)/(2-Outer side a))*((Outer side a+Inner Diagonal+Inner side d)/(2-Inner Diagonal))*((Outer side a+Inner Diagonal+Inner side d)/(2-Inner side d)))+ sqrt(((Outer side b+Inner Diagonal+Inner side c)/2)*((Side B+Diagonal+Side C)/(2-Side B))*((Outer side b+Inner Diagonal+Inner side c)/(2-Inner Diagonal))*((Outer side b+Inner Diagonal+Inner side c)/(2-Inner side c))) Go
Outer diagonal of Concave Quadrilateral
diagonal = sqrt((Side A^2)+(Side B^2)-(2*Side A*Side B)*cos(Angle B)) Go
Inner diagonal of Concave Quadrilateral
diagonal = sqrt((Side B^2)+(Side C^2)-(2*Side B*Side C)*cos(Angle C)) Go
Inner side of Concave Quadrilateral
side_d = sqrt(Side A^2+Diagonal^2-(2*Side A*Diagonal)*cos(Angle B)) Go
Acute angle of Concave Quadrilateral
angle_a = arccos((Side A^2+Side D^2-Diagonal^2)/(2*Side A*Side D)) Go
Reflex angle of Concave Quadrilateral
angle = (2*pi)-Angle A-Angle B-Angle C Go
Perimeter of concave quadrilateral
perimeter = Side A+Side B+Side C+Side D Go

### Area of Concave Quadrilateral Formula

area = sqrt(((Outer side a+Inner Diagonal+Inner side d)/2)*((Outer side a+Inner Diagonal+Inner side d)/(2-Outer side a))*((Outer side a+Inner Diagonal+Inner side d)/(2-Inner Diagonal))*((Outer side a+Inner Diagonal+Inner side d)/(2-Inner side d)))+ sqrt(((Outer side b+Inner Diagonal+Inner side c)/2)*((Side B+Diagonal+Side C)/(2-Side B))*((Outer side b+Inner Diagonal+Inner side c)/(2-Inner Diagonal))*((Outer side b+Inner Diagonal+Inner side c)/(2-Inner side c)))
A = sqrt(((a+f+d)/2)*((a+f+d)/(2-a))*((a+f+d)/(2-f))*((a+f+d)/(2-d)))+ sqrt(((b+f+c)/2)*((Sb+d+Sc)/(2-Sb))*((b+f+c)/(2-f))*((b+f+c)/(2-c)))

## What is a concave quadrilateral?

A quadrilateral is called a concave quadrilateral, if at least one line segment joining the vertices is not a part of the same region of the quadrilateral. That is, any line segment that joins two interior points goes outside the figure.

## How to Calculate Area of Concave Quadrilateral?

Area of Concave Quadrilateral calculator uses area = sqrt(((Outer side a+Inner Diagonal+Inner side d)/2)*((Outer side a+Inner Diagonal+Inner side d)/(2-Outer side a))*((Outer side a+Inner Diagonal+Inner side d)/(2-Inner Diagonal))*((Outer side a+Inner Diagonal+Inner side d)/(2-Inner side d)))+ sqrt(((Outer side b+Inner Diagonal+Inner side c)/2)*((Side B+Diagonal+Side C)/(2-Side B))*((Outer side b+Inner Diagonal+Inner side c)/(2-Inner Diagonal))*((Outer side b+Inner Diagonal+Inner side c)/(2-Inner side c))) to calculate the Area, The Area of Concave Quadrilateral formula is defined as A = √(a+f+d)/2 * ((a+f+d)/2-a) * ((a+f+d)/2-f) * ((a+f+d)/2-d) + √(b+c+f)/2 * ((b+c+f)/2-b) * ((b+c+f)/2-c) * ((b+c+f)/2-f) where a, b are outer sides, c, d are inner sides and f is diagonal of concave quadrilateral. Area and is denoted by A symbol.

How to calculate Area of Concave Quadrilateral using this online calculator? To use this online calculator for Area of Concave Quadrilateral, enter Outer side a (a), Inner diagonal (f), Inner side d (d), Outer side b (b), Inner side c (c), Side B (Sb), Diagonal (d) & Side C (Sc) and hit the calculate button. Here is how the Area of Concave Quadrilateral calculation can be explained with given input values -> 341.9251 = sqrt(((4.8+1.922+3.478)/2)*((4.8+1.922+3.478)/(2-4.8))*((4.8+1.922+3.478)/(2-1.922))*((4.8+1.922+3.478)/(2-3.478)))+ sqrt(((4+1.922+2.3)/2)*((7+8+4)/(2-7))*((4+1.922+2.3)/(2-1.922))*((4+1.922+2.3)/(2-2.3))).

### FAQ

What is Area of Concave Quadrilateral?
The Area of Concave Quadrilateral formula is defined as A = √(a+f+d)/2 * ((a+f+d)/2-a) * ((a+f+d)/2-f) * ((a+f+d)/2-d) + √(b+c+f)/2 * ((b+c+f)/2-b) * ((b+c+f)/2-c) * ((b+c+f)/2-f) where a, b are outer sides, c, d are inner sides and f is diagonal of concave quadrilateral and is represented as A = sqrt(((a+f+d)/2)*((a+f+d)/(2-a))*((a+f+d)/(2-f))*((a+f+d)/(2-d)))+ sqrt(((b+f+c)/2)*((Sb+d+Sc)/(2-Sb))*((b+f+c)/(2-f))*((b+f+c)/(2-c))) or area = sqrt(((Outer side a+Inner Diagonal+Inner side d)/2)*((Outer side a+Inner Diagonal+Inner side d)/(2-Outer side a))*((Outer side a+Inner Diagonal+Inner side d)/(2-Inner Diagonal))*((Outer side a+Inner Diagonal+Inner side d)/(2-Inner side d)))+ sqrt(((Outer side b+Inner Diagonal+Inner side c)/2)*((Side B+Diagonal+Side C)/(2-Side B))*((Outer side b+Inner Diagonal+Inner side c)/(2-Inner Diagonal))*((Outer side b+Inner Diagonal+Inner side c)/(2-Inner side c))). Outer side a is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back, Inner diagonal is a straight line joining two opposite corners of a square, rectangle, or another straight-sided shape, Inner side d is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back, Outer side b is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back, Inner side c is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back, Side B is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back, A diagonal is a straight line joining two opposite corners of a square, rectangle, or another straight-sided shape & Side C is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back.
How to calculate Area of Concave Quadrilateral?
The Area of Concave Quadrilateral formula is defined as A = √(a+f+d)/2 * ((a+f+d)/2-a) * ((a+f+d)/2-f) * ((a+f+d)/2-d) + √(b+c+f)/2 * ((b+c+f)/2-b) * ((b+c+f)/2-c) * ((b+c+f)/2-f) where a, b are outer sides, c, d are inner sides and f is diagonal of concave quadrilateral is calculated using area = sqrt(((Outer side a+Inner Diagonal+Inner side d)/2)*((Outer side a+Inner Diagonal+Inner side d)/(2-Outer side a))*((Outer side a+Inner Diagonal+Inner side d)/(2-Inner Diagonal))*((Outer side a+Inner Diagonal+Inner side d)/(2-Inner side d)))+ sqrt(((Outer side b+Inner Diagonal+Inner side c)/2)*((Side B+Diagonal+Side C)/(2-Side B))*((Outer side b+Inner Diagonal+Inner side c)/(2-Inner Diagonal))*((Outer side b+Inner Diagonal+Inner side c)/(2-Inner side c))). To calculate Area of Concave Quadrilateral, you need Outer side a (a), Inner diagonal (f), Inner side d (d), Outer side b (b), Inner side c (c), Side B (Sb), Diagonal (d) & Side C (Sc). With our tool, you need to enter the respective value for Outer side a, Inner diagonal, Inner side d, Outer side b, Inner side c, Side B, Diagonal & Side C and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Area?
In this formula, Area uses Outer side a, Inner diagonal, Inner side d, Outer side b, Inner side c, Side B, Diagonal & Side C. We can use 7 other way(s) to calculate the same, which is/are as follows -
• diagonal = sqrt((Side A^2)+(Side B^2)-(2*Side A*Side B)*cos(Angle B))
• diagonal = sqrt((Side B^2)+(Side C^2)-(2*Side B*Side C)*cos(Angle C))
• side_d = sqrt(Side A^2+Diagonal^2-(2*Side A*Diagonal)*cos(Angle B))
• angle_a = arccos((Side A^2+Side D^2-Diagonal^2)/(2*Side A*Side D))
• angle = (2*pi)-Angle A-Angle B-Angle C
• perimeter = Side A+Side B+Side C+Side D
• area = sqrt(((Outer side a+Inner Diagonal+Inner side d)/2)*((Outer side a+Inner Diagonal+Inner side d)/(2-Outer side a))*((Outer side a+Inner Diagonal+Inner side d)/(2-Inner Diagonal))*((Outer side a+Inner Diagonal+Inner side d)/(2-Inner side d)))+ sqrt(((Outer side b+Inner Diagonal+Inner side c)/2)*((Side B+Diagonal+Side C)/(2-Side B))*((Outer side b+Inner Diagonal+Inner side c)/(2-Inner Diagonal))*((Outer side b+Inner Diagonal+Inner side c)/(2-Inner side c)))
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