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Area of Concave Quadrilateral Formula

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Area of Concave Quadrilateral is the amount of two-dimensional space taken up by the Concave Quadrilateral. Check FAQs

A = \sqrt{(\frac{S First Outer + d Inner + S First Inner}{2}) \cdot ((\frac{S First Outer + d Inner + S First Inner}{2}) - S First Outer) \cdot ((\frac{S First Outer + d Inner + S First Inner}{2}) - d Inner) \cdot ((\frac{S First Outer + d Inner + S First Inner}{2}) - S First Inner)} + \sqrt{(\frac{S Second Outer + d Inner + S Second Inner}{2}) \cdot ((\frac{S Second Outer + d Inner + S Second Inner}{2}) - S Second Outer) \cdot ((\frac{S Second Outer + d Inner + S Second Inner}{2}) - d Inner) \cdot ((\frac{S Second Outer + d Inner + S Second Inner}{2}) - S Second Inner)}

A - Area of Concave Quadrilateral?S_{First Outer} - First Outer Side of Concave Quadrilateral?d_Inner - Inner Diagonal of Concave Quadrilateral?S_{First Inner} - First Inner Side of Concave Quadrilateral?S_{Second Outer} - Second Outer Side of Concave Quadrilateral?S_{Second Inner} - Second Inner Side of Concave Quadrilateral?

Area of Concave Quadrilateral Example

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Here is how the Area of Concave Quadrilateral equation looks like with Values.

Here is how the Area of Concave Quadrilateral equation looks like with Units.

Here is how the Area of Concave Quadrilateral equation looks like.

14.7284 = \sqrt{(\frac{10 + 4 + 7}{2}) \cdot ((\frac{10 + 4 + 7}{2}) - 10) \cdot ((\frac{10 + 4 + 7}{2}) - 4) \cdot ((\frac{10 + 4 + 7}{2}) - 7)} + \sqrt{(\frac{5 + 4 + 2}{2}) \cdot ((\frac{5 + 4 + 2}{2}) - 5) \cdot ((\frac{5 + 4 + 2}{2}) - 4) \cdot ((\frac{5 + 4 + 2}{2}) - 2)}

14.7284m² = \sqrt{(\frac{10m + 4m + 7m}{2}) \cdot ((\frac{10m + 4m + 7m}{2}) - 10m) \cdot ((\frac{10m + 4m + 7m}{2}) - 4m) \cdot ((\frac{10m + 4m + 7m}{2}) - 7m)} + \sqrt{(\frac{5m + 4m + 2m}{2}) \cdot ((\frac{5m + 4m + 2m}{2}) - 5m) \cdot ((\frac{5m + 4m + 2m}{2}) - 4m) \cdot ((\frac{5m + 4m + 2m}{2}) - 2m)}

14.7284 = \sqrt{(\frac{10 + 4 + 7}{2}) \cdot ((\frac{10 + 4 + 7}{2}) - 10) \cdot ((\frac{10 + 4 + 7}{2}) - 4) \cdot ((\frac{10 + 4 + 7}{2}) - 7)} + \sqrt{(\frac{5 + 4 + 2}{2}) \cdot ((\frac{5 + 4 + 2}{2}) - 5) \cdot ((\frac{5 + 4 + 2}{2}) - 4) \cdot ((\frac{5 + 4 + 2}{2}) - 2)}

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Area of Concave Quadrilateral Solution

Follow our step by step solution on how to calculate Area of Concave Quadrilateral?

FIRST Step Consider the formula

A = \sqrt{(\frac{S First Outer + d Inner + S First Inner}{2}) \cdot ((\frac{S First Outer + d Inner + S First Inner}{2}) - S First Outer) \cdot ((\frac{S First Outer + d Inner + S First Inner}{2}) - d Inner) \cdot ((\frac{S First Outer + d Inner + S First Inner}{2}) - S First Inner)} + \sqrt{(\frac{S Second Outer + d Inner + S Second Inner}{2}) \cdot ((\frac{S Second Outer + d Inner + S Second Inner}{2}) - S Second Outer) \cdot ((\frac{S Second Outer + d Inner + S Second Inner}{2}) - d Inner) \cdot ((\frac{S Second Outer + d Inner + S Second Inner}{2}) - S Second Inner)}

Next Step Substitute values of Variables

∴

A = \sqrt{(\frac{10m + 4m + 7m}{2}) \cdot ((\frac{10m + 4m + 7m}{2}) - 10m) \cdot ((\frac{10m + 4m + 7m}{2}) - 4m) \cdot ((\frac{10m + 4m + 7m}{2}) - 7m)} + \sqrt{(\frac{5m + 4m + 2m}{2}) \cdot ((\frac{5m + 4m + 2m}{2}) - 5m) \cdot ((\frac{5m + 4m + 2m}{2}) - 4m) \cdot ((\frac{5m + 4m + 2m}{2}) - 2m)}

Next Step Prepare to Evaluate

∴

A = \sqrt{(\frac{10 + 4 + 7}{2}) \cdot ((\frac{10 + 4 + 7}{2}) - 10) \cdot ((\frac{10 + 4 + 7}{2}) - 4) \cdot ((\frac{10 + 4 + 7}{2}) - 7)} + \sqrt{(\frac{5 + 4 + 2}{2}) \cdot ((\frac{5 + 4 + 2}{2}) - 5) \cdot ((\frac{5 + 4 + 2}{2}) - 4) \cdot ((\frac{5 + 4 + 2}{2}) - 2)}

Next Step Evaluate

∴

A = 14.7284175355899m²

LAST Step Rounding Answer

∴

A = 14.7284m²

Area of Concave Quadrilateral Formula Elements

Variables

Functions

Area of Concave Quadrilateral

Area of Concave Quadrilateral is the amount of two-dimensional space taken up by the Concave Quadrilateral.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Concave Quadrilateral

First Outer Side of Concave Quadrilateral

First Outer Side of Concave Quadrilateral is the first outermost side of the Concave Quadrilateral.

Symbol: S_{First Outer}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find First Outer Side of Concave Quadrilateral

Inner Diagonal of Concave Quadrilateral

Inner Diagonal of Concave Quadrilateral is a straight line joining two opposite corners, and lies inside the region of Concave Quadrilateral.

Symbol: d_Inner

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inner Diagonal of Concave Quadrilateral

First Inner Side of Concave Quadrilateral

First Inner Side of Concave Quadrilateral is the first innermost side of the Concave Quadrilateral.

Symbol: S_{First Inner}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find First Inner Side of Concave Quadrilateral

Second Outer Side of Concave Quadrilateral

Second Outer Side of Concave Quadrilateral is the second outermost side of the Concave Quadrilateral.

Symbol: S_{Second Outer}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Second Outer Side of Concave Quadrilateral

Second Inner Side of Concave Quadrilateral

Second Inner Side of Concave Quadrilateral is the second innermost side of the Concave Quadrilateral.

Symbol: S_{Second Inner}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Second Inner Side of Concave Quadrilateral

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Concave Quadrilateral category

Go Outer Diagonal of Concave Quadrilateral

d Outer = \sqrt{{S First Outer}^{2} + {S Second Outer}^{2} - (2 \cdot S First Outer \cdot S Second Outer \cdot \cos (∠ Second Acute))}

Go Inner Diagonal of Concave Quadrilateral

d Inner = \sqrt{{S Second Outer}^{2} + {S Second Inner}^{2} - (2 \cdot S Second Outer \cdot S Second Inner \cdot \cos (∠ Third Acute))}

Go First Inner Side of Concave Quadrilateral

S First Inner = \sqrt{{S First Outer}^{2} + {d Outer}^{2} - (2 \cdot S First Outer \cdot d Outer \cdot \cos (∠ Second Acute))}

Go First Acute Angle of Concave Quadrilateral

∠ First Acute = \arccos (\frac{{S First Outer}^{2} + {S First Inner}^{2} - {d Inner}^{2}}{2 \cdot S First Outer \cdot S First Inner})

How to Evaluate Area of Concave Quadrilateral?

Area of Concave Quadrilateral evaluator uses Area of Concave Quadrilateral = sqrt(((First Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+First Inner Side of Concave Quadrilateral)/2)*(((First Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+First Inner Side of Concave Quadrilateral)/2)-First Outer Side of Concave Quadrilateral)*(((First Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+First Inner Side of Concave Quadrilateral)/2)-Inner Diagonal of Concave Quadrilateral)*(((First Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+First Inner Side of Concave Quadrilateral)/2)-First Inner Side of Concave Quadrilateral))+sqrt(((Second Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+Second Inner Side of Concave Quadrilateral)/2)*(((Second Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+Second Inner Side of Concave Quadrilateral)/2)-Second Outer Side of Concave Quadrilateral)*(((Second Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+Second Inner Side of Concave Quadrilateral)/2)-Inner Diagonal of Concave Quadrilateral)*(((Second Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+Second Inner Side of Concave Quadrilateral)/2)-Second Inner Side of Concave Quadrilateral)) to evaluate the Area of Concave Quadrilateral, The Area of Concave Quadrilateral formula is defined as the total space occupied by the Concave Quadrilateral. Area of Concave Quadrilateral is denoted by A symbol.

How to evaluate Area of Concave Quadrilateral using this online evaluator? To use this online evaluator for Area of Concave Quadrilateral, enter First Outer Side of Concave Quadrilateral (S_{First Outer}), Inner Diagonal of Concave Quadrilateral (d_Inner), First Inner Side of Concave Quadrilateral (S_{First Inner}), Second Outer Side of Concave Quadrilateral (S_{Second Outer}) & Second Inner Side of Concave Quadrilateral (S_{Second Inner}) and hit the calculate button.

FAQs on Area of Concave Quadrilateral

What is the formula to find Area of Concave Quadrilateral?

The formula of Area of Concave Quadrilateral is expressed as Area of Concave Quadrilateral = sqrt(((First Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+First Inner Side of Concave Quadrilateral)/2)*(((First Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+First Inner Side of Concave Quadrilateral)/2)-First Outer Side of Concave Quadrilateral)*(((First Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+First Inner Side of Concave Quadrilateral)/2)-Inner Diagonal of Concave Quadrilateral)*(((First Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+First Inner Side of Concave Quadrilateral)/2)-First Inner Side of Concave Quadrilateral))+sqrt(((Second Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+Second Inner Side of Concave Quadrilateral)/2)*(((Second Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+Second Inner Side of Concave Quadrilateral)/2)-Second Outer Side of Concave Quadrilateral)*(((Second Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+Second Inner Side of Concave Quadrilateral)/2)-Inner Diagonal of Concave Quadrilateral)*(((Second Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+Second Inner Side of Concave Quadrilateral)/2)-Second Inner Side of Concave Quadrilateral)). Here is an example- 14.72842 = sqrt(((10+4+7)/2)*(((10+4+7)/2)-10)*(((10+4+7)/2)-4)*(((10+4+7)/2)-7))+sqrt(((5+4+2)/2)*(((5+4+2)/2)-5)*(((5+4+2)/2)-4)*(((5+4+2)/2)-2)).

How to calculate Area of Concave Quadrilateral?

With First Outer Side of Concave Quadrilateral (S_{First Outer}), Inner Diagonal of Concave Quadrilateral (d_Inner), First Inner Side of Concave Quadrilateral (S_{First Inner}), Second Outer Side of Concave Quadrilateral (S_{Second Outer}) & Second Inner Side of Concave Quadrilateral (S_{Second Inner}) we can find Area of Concave Quadrilateral using the formula - Area of Concave Quadrilateral = sqrt(((First Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+First Inner Side of Concave Quadrilateral)/2)*(((First Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+First Inner Side of Concave Quadrilateral)/2)-First Outer Side of Concave Quadrilateral)*(((First Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+First Inner Side of Concave Quadrilateral)/2)-Inner Diagonal of Concave Quadrilateral)*(((First Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+First Inner Side of Concave Quadrilateral)/2)-First Inner Side of Concave Quadrilateral))+sqrt(((Second Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+Second Inner Side of Concave Quadrilateral)/2)*(((Second Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+Second Inner Side of Concave Quadrilateral)/2)-Second Outer Side of Concave Quadrilateral)*(((Second Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+Second Inner Side of Concave Quadrilateral)/2)-Inner Diagonal of Concave Quadrilateral)*(((Second Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+Second Inner Side of Concave Quadrilateral)/2)-Second Inner Side of Concave Quadrilateral)). This formula also uses Square Root (sqrt) function(s).

Can the Area of Concave Quadrilateral be negative?

No, the Area of Concave Quadrilateral, measured in Area cannot be negative.

Which unit is used to measure Area of Concave Quadrilateral?

Area of Concave Quadrilateral is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Area of Concave Quadrilateral can be measured.

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Area of Concave Quadrilateral Formula

Area of Concave Quadrilateral Example

Area of Concave Quadrilateral Solution

Area of Concave Quadrilateral Formula Elements

Other formulas in Concave Quadrilateral category

How to Evaluate Area of Concave Quadrilateral?

FAQs on Area of Concave Quadrilateral

Variable Name