There are different units for perimeter and area The perimeter has the same units as the length of the sides of rectangle or square whereas the area's unit is squared. Area, A, is x times y. Video lesson Calculate the perimeter and the area in feet.
More classes on this subject Pre-Algebra Inequalities and one-step equations: Different ways to solve equations Pre-Algebra Inequalities and one-step equations: Understanding inequalities and equations. Search Math Playground All courses. All courses. The most well-known perimeter of a circle formula uses only one variable - circle radius:.
Have you ever wondered how many times your bike wheel will rotate on a ten-mile trip? Well, that's one of the cases where you'll need to use the circumference formula. Input the radius of your wheel half of the wheel's diameter , and divide 10 miles by the obtained circumference but don't forget about the convert the units of length! If you want to be even more accurate, you can include the size of the bike tire.
If you're keen cyclist, don't forget to have a look at our bike cadence and speed calculator and the gear calculator. Not convinced? Need more examples? How about calculating the icing around your circular birthday cake , or you can find how much lace you need to sew your circle skirt.
Calculating the perimeter of a circle sector may sound tricky - is it only the arc length or is it the arc length plus two radii?
Just keep in mind perimeter definition! The sector perimeter is the sum of the lengths of all its boundaries, so it's the latter:. Although the formula for the area of an ellipse is really simple and easy to remember, the perimeter of an ellipse formula is the most troublesome of all the equations listed here. We've chosen to implement one of the Ramanujan approximations in this perimeter calculator:.
Where a is the shortest possible radius and b in the longest possible radius of an ellipse. The other, more accurate Ramanujan approximation is:.
If you want to calculate the perimeter of an irregular trapezoid, there's no special formula - just add all four sides:. There's also an option that that presents itself with certain special trapezoids - like an isosceles trapezoid, where you need a, b, and c sides. Another example is a right trapezoid, where the length of the bases and one leg are enough to find the shape's perimeter the last leg is calculated using Pythagoras' Theorem. In this perimeter calculator you'll find three formulas for the perimeter of a parallelogram :.
The perimeter of a rhombus formula is not rocket science, so let's make it concise - it's the same as the perimeter of a square formula! Try deriving the formula yourself. You know that the two diagonals of a rhombus are perpendicular to and bisect each other, so you can divide the shape into four congruent right triangles.
Then multiply the result by four to find the final perimeter of a rhombus formula. Notice that the perimeter of a rectangle always has two pairs of equal length sides. Area of Parallelograms. The area of a two-dimensional figure describes the amount of surface the shape covers.
You measure area in square units of a fixed size. Examples of square units of measure are square inches, square centimeters, or square miles. When finding the area of a polygon, you count how many squares of a certain size will cover the region inside the polygon.
You can count that there are 16 squares, so the area is 16 square units. It could take a long time to count. Fortunately, you can use multiplication. To help you find the area of the many different categories of polygons, mathematicians have developed formulas. These formulas help you find the measurement more quickly than by simply counting. The formulas you are going to look at are all developed from the understanding that you are counting the number of square units inside the polygon.
You can count the squares individually, but it is much easier to multiply 3 times 5 to find the number more quickly. And, more generally, the area of any rectangle can be found by multiplying length times width. Find the area. Start with the formula for the area of a rectangle, which multiplies the length times the width.
Substitute 8 for the length and 3 for the width. Be sure to include the units, in this case square cm. It would take 24 squares, each measuring 1 cm on a side, to cover this rectangle. Notice in a rectangle, the length and the width are perpendicular. This should also be true for all parallelograms. Base b for the length of the base , and height h for the width of the line perpendicular to the base is often used.
Find the area of the parallelogram. Start with the formula for the area of a parallelogram:. Substitute the values into the formula. The area of the parallelogram is 8 ft 2. Find the area of a parallelogram with a height of 12 feet and a base of 9 feet.
It looks like you added the dimensions; remember that to find the area, you multiply the base by the height. The correct answer is ft 2. It looks like you multiplied the base by the height and then divided by 2. To find the area of a parallelogram, you multiply the base by the height. This would give you the perimeter of a 12 by 9 rectangle.
The height of the parallelogram is 12 and the base of the parallelogram is 9; the area is 12 times 9, or ft 2. Area of Triangles and Trapezoids. The formula for the area of a triangle can be explained by looking at a right triangle.
Look at the image below—a rectangle with the same height and base as the original triangle. The area of the triangle is one half of the rectangle! When you use the formula for a triangle to find its area, it is important to identify a base and its corresponding height, which is perpendicular to the base. A triangle has a height of 4 inches and a base of 10 inches.
Start with the formula for the area of a triangle. Substitute 10 for the base and 4 for the height. To find the area of a trapezoid, take the average length of the two parallel bases and multiply that length by the height:. An example is provided below. Notice that the height of a trapezoid will always be perpendicular to the bases just like when you find the height of a parallelogram.
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