Content

• Steps
• Advice
• Warning

There are many reasons why you might want to know the area of ​​some geometry. Maybe you're doing your homework or want to know how much paint to buy to repaint your room, whatever the reason, wikiHow will help! Start with Step 1 below to learn how to calculate the area of ​​geometries.

Steps

Method 1 of 7: Square, rectangle, and parallelogram

1. 

   Measure width and height. First you need to find the width and height of the shape (in other words, find the measure of two adjacent sides).
   • For parallelograms, you need to use base edge and height, which is similar to width and height.
   • You will actually have to measure it yourself, but for homework your teacher has these measurements on the drawing.

2. 

   
   
   Multiply the side lengths together. For example, if you had a rectangle with a height of 16 cm and a width of 42 cm, you would multiply 16 x 42.
   • If you calculate the area of ​​a square, you can save time by using a calculator and squaring an edge. If the length of the side is 4 cm, press 4 and then press the square button on the calculator to get your answer. Square means multiplying that number by itself.

3. 

   
   
   Find out the results. The result from multiplication is the area of ​​the figure, enclosed with the "square unit". Hence the area of ​​the rectangle will be 672 square centimeters.
   • Unit area is also abbreviated as a small number 2 above the length symbol to replace the word "square".
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Method 2 of 7: Trapezoid

1. 

   
   
   Find the lengths of the sides. You need the lengths of the base, top edge, and height. The bottom and top edge are two parallel sides, while the height line is the segment perpendicular to the two sides.
   • You will actually have to measure it yourself, but for homework your teacher has these measurements on the drawing.

2. 

   Add up the bottom and top edge measurements. Let's say our trapezoid has side 5 cm above and base side 7 cm. The result of addition is 12.

3. 

   Multiply that value by 1/2. The result of this calculation is 6.

4. 

   Multiply that value by the height. For this trapezoid, assume a height of 6 cm. The result of the calculation is 36.

5. 

   Find out the results. The number you get after multiplying by the height is the area of ​​the trapezoid. Therefore, the trapezoid 5x6x7 has an area of ​​36 square centimeters. advertisement

Method 3 of 7: Circle

1. 

   Find the radius. To find the area of ​​a circle, you need a radius length. It is the length of the line connecting the center of the circle to a point on the circle. You can also find the radius by dividing the diameter in half.
   • You will actually have to measure it yourself, but for homework your teacher has these measurements on the drawing.

2. 

   Square the radius. Multiply the radius length by itself. Suppose we have a radius of 8 meters. The result of multiplication is 64.

3. 

   Multiply by pi. Pi (π) is a number commonly used in many calculations. If you are using a calculator, press the pi button for accurate results. If you don't have a calculator, you can round pi (omit a few odd decimal places) and simply multiply by 3.14159. The result of the calculation is 201,06176.

4. 

   Find out the results. So we have the area of ​​the circle which is 201.06176 square meters. advertisement

Method 4 of 7: Fan-shaped

1. 

   Find the required measurements. The fan shape is part of the circle and looks like a handheld fan. You need to know the radius of the original circle, or one side of the “fan shape,” and the angle made up of the two fan-shaped edges. Suppose we have a radius of 14 cm and the angle between the two radii is 60 degrees.
   • You will actually have to measure it yourself, but for homework your teacher has these measurements on the drawing.

2. 

   Square the radius. Multiply the radius length by itself. The result of this multiplication is 196 (14x14).

3. 

   Multiply by pi. Pi (π) is a number commonly used in many calculations. If you are using a calculator, press the pi button for accurate results. If you don't have a calculator, you can round pi (omit a few odd decimal places) and simply multiply by 3.14159. The result of this calculation is 615,75164.

4. 

   Divide the angle by 360. Now you need to divide the angle by 360 (the number of degrees of a circle). For this problem we get 0.166. It's actually a periodic number, but we rounded it up to make it easier to calculate.

5. 

   Multiply this value by the value previously obtained. Multiply the number you get when dividing by 360 by the number you found earlier after multiplying by pi. The result of the calculation is 102,214.

6. 

   Find out the results. So we have the area of ​​the fan shape is 102,214 square centimeters. advertisement

Method 5 of 7: Ellipse

1. 

   Find measurements. To calculate the area of ​​an ellipse, you need to know two "radii" that can be thought of as half the width and height of the ellipse. These are lines from the center of the ellipse to the midpoint of the long edge and from the center of the ellipse to the midpoint of the short edge. These two segments will be perpendicular to each other.
   • You will actually have to measure it yourself, but for homework your teacher has these measurements on the drawing.

2. 

   Multiply the two radii together. Let's say our ellipse has a width of 6 cm and a height of 4 cm. The two radii will be 3 cm and 2 cm, respectively. Now we multiply these two numbers to get 6 (3x2).

3. 

   Multiply that value by pi. Pi (π) is a number commonly used in many calculations. If you are using a calculator, press the pi button for accurate results.If you don't have a calculator, you can round pi (omit a few odd decimal places) and simply multiply by 3.14159. The result of this multiplication is 18,84954.

4. 

   Find out the results. So we have an elliptical area of ​​18,84954 square centimeters. advertisement

Method 6 of 7: Triangles

1. 

   Find measurements. You need to know the measure of the base and the height of the triangle. The bottom edge is any side of the triangle at which the altitude can be calculated. Suppose we have a triangle with a base of 3 meters and the height of 1 meter.
   • You will actually have to measure it yourself, but for homework your teacher has these measurements on the drawing.

2. 

   Multiply the bottom edge by the height. The result of the calculation is 3 (3x1).

3. 

   Multiply that value by 1/2. The result is 1.5.

4. 

   Find out the results. So the area of ​​the triangle is 1.5 square meters. advertisement

Method 7 of 7: Complex shapes

1. 

   Divide the shape into sections. To calculate the area of ​​complex shapes, you must divide it into several smaller shapes with the standard geometric shapes above. For this example exercise, you probably already have a clear view of what those shapes are, but in reality you need to divide them into many smaller shapes to get the exact area.
   • Initially, you will find right angles and parallel sides. That is the basis of many shapes.

2. 

   Calculate the area of ​​individual shapes. Use the instructions above to find the areas of different shapes.

3. 

   Add the shapes together. Add the areas of the shapes together to get the area of ​​the original shape.

4. 

   Use other methods. There are other tips for calculating the area, depending on what your shape looks like. You can also add an imaginary area to a standard geometry, and then subtract the area of ​​the fantasy from the total area. advertisement

Advice

• Use this calculator if needed and when you want to see how the problem is solved.
• Ask a friend for help if you get stuck!

Warning

• Remember to use one unit of measure consistently to avoid confusing numbers!
• You'd better check the results once you're done!