Difference between revisions of "Find the Area of a Quadrilateral"
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#*'''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'''. | #*'''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. | #* 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. | ||
| − | #Multiply one side by itself to find the area of a square. 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:<ref>http://www.dummies.com/how-to/content/how-to-calculate-the-area-of-a-quadrilateral.html</ref> | + | #Multiply one side by itself to find the area of a square. 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:<ref name="rf16733">http://www.dummies.com/how-to/content/how-to-calculate-the-area-of-a-quadrilateral.html</ref> |
#*'''''Area = side × side''''' or '''''A = s<sup>2</sup>''''' | #*'''''Area = side × side''''' or '''''A = s<sup>2</sup>''''' | ||
#*'''Example:''' If one side of a square has a length of 4 feet, (t = 4), then the area of this square is simply t<sup>2</sup>, or 4 x 4 = '''16 square feet'''. | #*'''Example:''' If one side of a square has a length of 4 feet, (t = 4), then the area of this square is simply t<sup>2</sup>, or 4 x 4 = '''16 square feet'''. | ||
| − | #Multiply the diagonals and divide by two to find the area of a rhombus. 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: <ref>http://www.mathopenref.com/rhombusarea.html</ref> | + | #Multiply the diagonals and divide by two to find the area of a rhombus. 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: <ref name="rf16734">http://www.mathopenref.com/rhombusarea.html</ref> |
#*'''''Area = (Diag. 1 × Diag. 2)/2''''' or '''''A = (d<sub>1</sub> × d<sub>2</sub>)/2''''' | #*'''''Area = (Diag. 1 × Diag. 2)/2''''' or '''''A = (d<sub>1</sub> × d<sub>2</sub>)/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. | #* '''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. | ||
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#Know how to identify a trapezoid. A trapezoid is a quadrilateral with at least two sides that run parallel to each other. Its corners can have any angles. Each of the four sides on a trapezoid can be a different length. | #Know how to identify a trapezoid. A trapezoid is a quadrilateral with at least two sides that run parallel to each other. Its corners can have any angles. Each of the four sides on a trapezoid can be a different length. | ||
#* There are two different ways you can find the area of a trapezoid, depending on which pieces of information you have. Below, you'll see how to use both. | #* There are two different ways you can find the area of a trapezoid, depending on which pieces of information you have. Below, you'll see how to use both. | ||
| − | #Find the height of the trapezoid. The height of a trapezoid is the perpendicular line connecting the two parallel sides. This will ''not'' usually be the same length as one of the sides, because the sides are usually pointed diagonally. You will need this for both area equations. Here's how to find the height of a trapezoid:<ref>http://www.mathgoodies.com/lessons/vol1/area_trapezoid.html</ref> | + | #Find the height of the trapezoid. The height of a trapezoid is the perpendicular line connecting the two parallel sides. This will ''not'' usually be the same length as one of the sides, because the sides are usually pointed diagonally. You will need this for both area equations. Here's how to find the height of a trapezoid:<ref name="rf16735">http://www.mathgoodies.com/lessons/vol1/area_trapezoid.html</ref> |
#* Find the shorter of the two base lines (the parallel sides). Place your pencil at the corner between that baseline and one of the non-parallel sides. Draw a straight line that meets the two base lines at right angles. Measure this line to find the height. | #* Find the shorter of the two base lines (the parallel sides). Place your pencil at the corner between that baseline and one of the non-parallel sides. Draw a straight line that meets the two base lines at right angles. Measure this line to find the height. | ||
#* You can also sometimes use trigonometry to determine the height if the height line, the base, and the other side make a right triangle. See [[Use Right Angled Trigonometry|our trig article]] for more information. | #* You can also sometimes use trigonometry to determine the height if the height line, the base, and the other side make a right triangle. See [[Use Right Angled Trigonometry|our trig article]] for more information. | ||
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#*'''Example:''' If a kite has diagonals with lengths of 19 meters and 5 meters, then its area is simply (19 × 5)/2 = '''95/2 = 47.5 square meters'''. | #*'''Example:''' If a kite has diagonals with lengths of 19 meters and 5 meters, then its area is simply (19 × 5)/2 = '''95/2 = 47.5 square meters'''. | ||
#* If you don't know the lengths of the diagonals and can't measure them, you can use trigonometry to calculate them. See [http://www.wikihow.com/Find-the-Area-of-a-Kite#Area_of_a_Diamond_Kite_using_Trigonometry_sub our kite article] for more information. | #* If you don't know the lengths of the diagonals and can't measure them, you can use trigonometry to calculate them. See [http://www.wikihow.com/Find-the-Area-of-a-Kite#Area_of_a_Diamond_Kite_using_Trigonometry_sub our kite article] for more information. | ||
| − | #Use the lengths of the sides and the angle between them to find the area. If you know the two different values for the lengths of the sides and the angle at the corner between those sides, you can solve for the area of the kite with the principles of trigonometry.<ref>http://www.mathopenref.com/kitearea.html</ref> This method requires you to know how to do sine functions (or at least to have a calculator with a sine function). See [[Use Right Angled Trigonometry|our trig article]] for more information or use the formula below: | + | #Use the lengths of the sides and the angle between them to find the area. If you know the two different values for the lengths of the sides and the angle at the corner between those sides, you can solve for the area of the kite with the principles of trigonometry.<ref name="rf16736">http://www.mathopenref.com/kitearea.html</ref> This method requires you to know how to do sine functions (or at least to have a calculator with a sine function). See [[Use Right Angled Trigonometry|our trig article]] for more information or use the formula below: |
#*'''''Area = (Side 1 × Side 2) × sin (angle)''''' or '''''A = (s<sub>1</sub> × s<sub>2</sub>) × sin(θ)''''' (where θ is the angle between sides 1 and 2). | #*'''''Area = (Side 1 × Side 2) × sin (angle)''''' or '''''A = (s<sub>1</sub> × s<sub>2</sub>) × sin(θ)''''' (where θ is the angle between sides 1 and 2). | ||
#* '''Example:''' You have a kite with two sides of length 6 feet and two sides of length 4 feet. The angle between them is about 120 degrees. In this case, you can solve for the area like this: (6 × 4) × sin(120) = 24 × 0.866 = '''20.78 square feet''' | #* '''Example:''' You have a kite with two sides of length 6 feet and two sides of length 4 feet. The angle between them is about 120 degrees. In this case, you can solve for the area like this: (6 × 4) × sin(120) = 24 × 0.866 = '''20.78 square feet''' | ||
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== Tips == | == Tips == | ||
| − | * [http://www.handymath.com/cgi-bin/irregangle12.cgi?submit=Entry This triangle calculator] can be handy for making the calculations in the "Any Quadrilateral" method above.<ref>http://www.handymath.com/cgi-bin/irregangle12.cgi?submit=Entry</ref> | + | * [http://www.handymath.com/cgi-bin/irregangle12.cgi?submit=Entry This triangle calculator] can be handy for making the calculations in the "Any Quadrilateral" method above.<ref name="rf16737">http://www.handymath.com/cgi-bin/irregangle12.cgi?submit=Entry</ref> |
* For more information, see our shape-specific articles: [[Find the Area of a Square|How to Find the Area of a Square]], [[Calculate the Area of a Rectangle|How to Calculate the Area of a Rectangle]], [[Calculate the Area of a Rhombus|How to Calculate the Area of a Rhombus]], [[Calculate the Area of a Trapezoid|How to Calculate the Area of a Trapezoid]], and [[Find the Area of a Kite|How to Find the Area of a Kite]] | * For more information, see our shape-specific articles: [[Find the Area of a Square|How to Find the Area of a Square]], [[Calculate the Area of a Rectangle|How to Calculate the Area of a Rectangle]], [[Calculate the Area of a Rhombus|How to Calculate the Area of a Rhombus]], [[Calculate the Area of a Trapezoid|How to Calculate the Area of a Trapezoid]], and [[Find the Area of a Kite|How to Find the Area of a Kite]] | ||
