How to Find the Area of a Quadrilateral
Know how to identify a parallelogram., Multiply base times height to get the area of a rectangle., Multiply one side by itself to find the area of a square., Multiply the diagonals and divide by two to find the area of a rhombus., Alternatively, use...
Step-by-Step Guide
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Step 1: Know how to identify a parallelogram.
A parallelogram is any four-sided shape with two pairs of parallel sides where the sides across from each other are the same length.
Parallelograms include:
Squares:
Four sides, all the same length.
Four corners, all 90 degrees (right angles).
Rectangles:
Four sides; opposite sides have same lengths.
Four corners, all 90 degrees.
Rhombuses:
Four sides; opposite sides have same lengths.
Four corners; none have to be 90 degrees but opposite corners must have the same angles. , To find the area of a rectangle, you need two measurements: the width, or base (the longer side of the rectangle), and the length, or height (the shorter side of the rectangle).
Then, just multiply them together to get the area.
In other words:
Area = base × height, or A = b × h for short.
Example:
If the base of a rectangle has a length of 10 inches and the height has a length of 5 inches, then the area of the rectangle is simply 10 × 5 (b × h) = 50 square inches.
Don't forget that when you're finding a shape's area, you will use square units (square inches, square feet, square meters, etc.) for your answer. , Squares are basically special rectangles, so you can use the same formula to find their area.
However, since a square's sides all have the same length, you can use the shortcut of just multiplying one side's length by itself.
This is the same as multiplying the square's base by its height because the base and height are simply always the same.
Use the following equation:
Area = side × side or A = s2 Example:
If one side of a square has a length of 4 feet, (t = 4), then the area of this square is simply t2, or 4 x 4 = 16 square feet. , Be careful with this one — when you're finding the area of a rhombus, you can't simply multiply two adjacent sides.
Instead, find the diagonals (the lines connecting each set of opposite corners), multiply them, and divide by two.
In other words:
Area = (Diag. 1 × Diag. 2)/2 or A = (d1 × d2)/2 Example:
If a rhombus has diagonals with a length of 6 meters and 8 meters, then its area is simply (6 × 8)/2 = 48/2 = 24 square meters. , Technically, you can also use the base times height formula to find the area of a rhombus.
Here, "base" and "height" don't mean you can just multiply two adjacent sides, however.
First, pick one side to be the base.
Then, draw a line from the base to the opposite side.
The line should meet both sides at 90 degrees.
The length of this side is what you should use for height.
Example:
A rhombus has sides of 10 miles and 5 miles.
The straight-line distance between the 10 mile (16.1 km) sides is 3 miles (4.8 km).
If you want to find the area of the rhombus, you would multiply 10 × 3 = 30 square miles. , The side × side formula given above for squares is by far the most convenient way to find the area for these shapes.
However, because squares are technically both rectangles and rhombuses as well as squares, you can use those shapes' area formulas for squares and get the correct answer.
In other words, for squares:
Area = base × height or A = b × h Area = (Diag. 1 × Diag. 2)/2 or A = (d1 × d2)/2 Example:
A four-sided shape has two adjacent sides with lengths of 4 meters.
You can find the area of this square by multiplying its base times its height: 4 × 4 = 16 square meters.
Example:
A square's diagonals are both equal to 10 centimeters.
You can find this square's area with the diagonal formula: (10 × 10)/2 = 100/2 = 50 square centimeters. -
Step 2: Multiply base times height to get the area of a rectangle.
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Step 3: Multiply one side by itself to find the area of a square.
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Step 4: Multiply the diagonals and divide by two to find the area of a rhombus.
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Step 5: Alternatively
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Step 6: use base × height to find the area of a rhombus.
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Step 7: Be aware that the rhombus and rectangle formulas work for squares.
Detailed Guide
A parallelogram is any four-sided shape with two pairs of parallel sides where the sides across from each other are the same length.
Parallelograms include:
Squares:
Four sides, all the same length.
Four corners, all 90 degrees (right angles).
Rectangles:
Four sides; opposite sides have same lengths.
Four corners, all 90 degrees.
Rhombuses:
Four sides; opposite sides have same lengths.
Four corners; none have to be 90 degrees but opposite corners must have the same angles. , To find the area of a rectangle, you need two measurements: the width, or base (the longer side of the rectangle), and the length, or height (the shorter side of the rectangle).
Then, just multiply them together to get the area.
In other words:
Area = base × height, or A = b × h for short.
Example:
If the base of a rectangle has a length of 10 inches and the height has a length of 5 inches, then the area of the rectangle is simply 10 × 5 (b × h) = 50 square inches.
Don't forget that when you're finding a shape's area, you will use square units (square inches, square feet, square meters, etc.) for your answer. , Squares are basically special rectangles, so you can use the same formula to find their area.
However, since a square's sides all have the same length, you can use the shortcut of just multiplying one side's length by itself.
This is the same as multiplying the square's base by its height because the base and height are simply always the same.
Use the following equation:
Area = side × side or A = s2 Example:
If one side of a square has a length of 4 feet, (t = 4), then the area of this square is simply t2, or 4 x 4 = 16 square feet. , Be careful with this one — when you're finding the area of a rhombus, you can't simply multiply two adjacent sides.
Instead, find the diagonals (the lines connecting each set of opposite corners), multiply them, and divide by two.
In other words:
Area = (Diag. 1 × Diag. 2)/2 or A = (d1 × d2)/2 Example:
If a rhombus has diagonals with a length of 6 meters and 8 meters, then its area is simply (6 × 8)/2 = 48/2 = 24 square meters. , Technically, you can also use the base times height formula to find the area of a rhombus.
Here, "base" and "height" don't mean you can just multiply two adjacent sides, however.
First, pick one side to be the base.
Then, draw a line from the base to the opposite side.
The line should meet both sides at 90 degrees.
The length of this side is what you should use for height.
Example:
A rhombus has sides of 10 miles and 5 miles.
The straight-line distance between the 10 mile (16.1 km) sides is 3 miles (4.8 km).
If you want to find the area of the rhombus, you would multiply 10 × 3 = 30 square miles. , The side × side formula given above for squares is by far the most convenient way to find the area for these shapes.
However, because squares are technically both rectangles and rhombuses as well as squares, you can use those shapes' area formulas for squares and get the correct answer.
In other words, for squares:
Area = base × height or A = b × h Area = (Diag. 1 × Diag. 2)/2 or A = (d1 × d2)/2 Example:
A four-sided shape has two adjacent sides with lengths of 4 meters.
You can find the area of this square by multiplying its base times its height: 4 × 4 = 16 square meters.
Example:
A square's diagonals are both equal to 10 centimeters.
You can find this square's area with the diagonal formula: (10 × 10)/2 = 100/2 = 50 square centimeters.
About the Author
Nancy Gomez
Enthusiastic about teaching hobbies techniques through clear, step-by-step guides.
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