Area in math circles in rectangle full#

Area of a Square Inside a Circle Example 3įind the area of the shaded parts of the circle that are outside square below. To find the area of the square we need to work out 2r 2, where r=6 in. In this case, the diameter of the circle is known, which is equal to twice the value of the radius. Area of a Square Inside a Circle Example 2 To find the area of the square we need to work out 2r 2, where r=4cm. We can also say that the perimeter of the square is 4 x √2 r = 4√2 r Square Inside a Circle Area ExamplesĪrea of a Square Inside a Circle Example 1 So the Area of the Square Inside the Circle is 2r 2 The area of the square can now simply be found by multiplying two adjacent sides together to give: Pythagoras' theorem states that the sum of the squares of the two smaller sides of the triangle is equal to the square of the hypotenuse (which in this case is equal to 2r).Īs s is the vaue for the side of the square, this gives us: Let's look closely at the right triangle that has been made by the diagonal of the square:Īs the triangle is a right triangle, we can use Pythagoras' theorem to find the missing side s. You can also see that the diagonal and two sides of the square into two right triangles. This means that the length of the diagonal is 2r, where r is the radius of the circle. You will notice that the diagonal of the square is also the diameter of the circle as the diagonal goes from one side of the circle to the other through the center.

Let's start by looking at the four corners of the square and draw in one of the diagonals. So, the circumference of the circle is 31.4 mm.For those of you who like to know how things work, and why the formula is 2r 2, we will show you how it can be found below! What is the circumference of a circle whose area is 78.5 mm 2? It is possible to calculate the area of a circle given its circumference.įind the area of a circle whose circumference is 25.12 cm. Area of a circle using the circumferenceĪs we already know, the circumference of a circle is the distance around a circle. Thus, the diameter of the circle will be 14.1 m. Therefore, the dimensions of the square plate will be 17.72 cm by 17.72 cm.įind the diameter of a circle with an area of 156 m 2. Find the dimensions of a square plate that will have the same area as the circular plate.Įquate the area of the circle to the area of the squareįind the square root of both sides to get, The diameter of a circular plate is 20 cm.

So, the area of the circle with a diameter of 6 inches is 28.26 square inches.Ĭalculate the area of a dinner plate, which has a diameter of 10 cm. When the diameter of a circle is known, the area of the circle is given by,įind the area of a circle with a diameter of 6 inches. Therefore, the area of the sprinkled lawn is 314 sq. Lawn sprinkler sprays water 10 feet in every direction as it rotates. Since the radius cannot have a negative value, we take positive 9 as the correct answer. The area of a circle is 254.34 square yards.

Let’s get a better understanding of this formula by working out a few example problems.įind the area of a circle whose radius is 15 mm.Ĭalculate the area of the circle shown below. Pi (π) = 22/7 or 3.14 and r = the radius of a circle. Given the radius of a circle, the formula for calculating the area of a circle states that: Let us discuss these formulas for finding the area of a circle. These formulas are applied depending on the information you are given. The area of a circle can be calculated using three formulas. We can measure the area of a circle in m 2, km 2, in 2, mm 2, etc.

Area in math circles in rectangle full#

Then, the total number of full squares located inside the circle represents the area of the circle. In simple words, the area of a circle is the total number of square units inside that circle.įor example, if you draw squares of dimensions 1cm by 1cm inside a circle. The area of the circle is the measure of the space or region enclosed inside the circle. In this article, you will learn the area of a circle and the formulas for calculating the area of a circle. To recall, the area is the region that occupied the shape in a two-dimensional plane.