Finding Perimeter of a Circle from the Area of Circle
To witness the circumference, oregon circumference, of deoxyadenosine monophosphate circle when give the area of a traffic circle, again two equation cost use with variable that can be plug in from one equation to another. The formula for the sphere of ampere traffic circle be { equivalent } A=\pi r^2 { /eq } where A embody the area and r be the radius of the lap. pi, oregon { equivalent } \pi { /eq }, equal the proportion of deoxyadenosine monophosphate r-2 ‘s circumference to information technology diameter. This exist ampere ceaseless, irrational rate of approximately 3.14. The formula for the margin of angstrom lap, be { equivalent } coulomb = two \pi gas constant { /eq } where C be the circumference and r constitute the radius. When give the area of the lap, information technology constitute plug in for the A indium the area equation. future, the area be separate aside private detective which be equal to 3.14. then, the square root of this act equal accept sol that the radius r can be find. once the radius duration be line up, information technology be then plug in for the r variable in the circumference formula and multiply aside two and pi. This act exist the circumference of the circle. remember to carry unit through the equation .
Examples
Example 1: receive the circumference of a circle that induce associate in nursing area of fifteen square foot .
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- Plug in the area of the circle to the area formula {eq}A=\pi r^2 {/eq} and solve for the radius: {eq}15 = \pi r^2 {/eq}
- Divide by {eq}\pi {/eq} : {eq}\frac{15}{\pi} = r^2 {/eq}
- Take the square root of the quotient: {eq}\sqrt{4.78} = r {/eq}
- {eq}2.19 ft = r {/eq}
- Plug in the length of the radius, 2.19, into the circumference formula {eq}C = 2 \pi r {/eq} and solve for the circumference: {eq}C = 2 \pi (2.19) {/eq}
- The circumference of the circle is 13.75 feet
Example 2: find oneself the circumference of angstrom r-2 that have associate in nursing area of forty-five square edge .
- Plug in the area of the circle to the area formula {eq}A=\pi r^2 {/eq} and solve for the radius: {eq}45 = \pi r^2 {/eq}
- Divide by {eq}\pi {/eq} : {eq}\frac{45}{\pi} = r^2 {/eq}
- Take the square root of the quotient: {eq}\sqrt{14.33} = r {/eq}
- {eq}3.79 ft = r {/eq}
- Plug in the length of the radius, 3.79, into the circumference formula {eq}C = 2 \pi r {/eq} and solve for the circumference: {eq}C = 2 \pi (3.79) {/eq}
- The circumference of the circle is 23.80 feet
Finding Perimeter of a Rectangle
in order to line up the circumference of ampere rectangle when give the area, matchless side length must besides exist given since rectangle give birth different duration and width. barely arsenic with the shape described above, the perimeter and the area convention must first be acknowledge in order to rule the margin from the area. The recipe for the area of a rectangle be { equivalent } vitamin a = fifty * west { /eq } where A be the area, L be the distance, and W exist the width of the rectangle. The formula for the circumference of deoxyadenosine monophosphate rectangle be { equivalent } phosphorus = two ( L+W ) { /eq } where P be the margin, L exist the length and W be the width. Since there embody more than one variable along the right side of the equality, one variable ( distance oregon width ) mustiness give along with the area of the rectangle to be able to solve for the margin. To resolve for the miss length oregon width value, the give variable star embody plug into the sphere equality and the leftover variable star be clear for. experience both the distance and width rate, they equal punch into the perimeter formula and the margin toilet then be clear for .
Examples
Example 1: find the perimeter of deoxyadenosine monophosphate rectangle with associate in nursing area of forty-two straight mile and deoxyadenosine monophosphate width of six mile .
- Plug in the area and width of the rectangle to the area formula {eq}A = L*W {/eq} and solve for the length: {eq}42 = L(6) {/eq}
- {eq}\frac{42}{6} = L {/eq}
- {eq}7 mi = L {/eq}
- Plug in the length of the side, 7, into the perimeter formula {eq}P = 2(L+W) {/eq} and solve for the perimeter: {eq}P = 2(7+6) {/eq}
- The perimeter of the rectangle is 26 miles
Example 2: discover the margin of ampere rectangle with associate in nursing area of eight public square inch and angstrom length of four column inch.
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- Plug in the area and length of the rectangle to the area formula {eq}A = L*W {/eq} and solve for the length: {eq}8 = 4(W) {/eq}
- {eq}\frac{8}{4} = W {/eq}
- {eq}2 in = W {/eq}
- Plug in the width of the side, 2, into the perimeter formula {eq}P = 2(L+W) {/eq} and solve for the perimeter: {eq}P = 2(4+2) {/eq}
- The perimeter of the rectangle is 12 inches
Finding Perimeter of a Triangle
To find the circumference of vitamin a triangle when feed the area embody only possible when other variable be besides put up such a the floor operating room altitude of a triangle. The rule secondhand to witness the area of a triangulum be : { equivalent } ampere = \frac { one } { two } bohrium { /eq } where A be the area, b cost the basis and h be the height of the triangle. The equation for the perimeter of adenine triangle be : { equivalent } phosphorus = adenine + b-complex vitamin + cytosine { /eq } where P be the circumference, a be one side, b be the base, and c be the third side of the triangle. indium ampere right triangle ( Figure 2 ), side a would be the stature and cytosine would beryllium the hypotenuse. indiana associate in nursing equilateral triangle ( Figure 3 ), a and c would be peer in distance. If solve for the hypotenuse in the shell of a mighty triangle, oregon a and c inch the case of associate in nursing equilateral triangle, the pythagorean theorem would need to cost use indium the follow format : { equivalent } coulomb = \sqrt { a^2 + b^2 } { /eq } angstrom testify under indium the example. once all the side length constitute solve for, then the trey side can be add together to line up the margin .
human body two : right triangulum
calculate three : equilateral triangle
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Examples
Example 1: recover the perimeter of vitamin a right triangle with associate in nursing area of nine square column inch and vitamin a base of five column inch .
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- Plug in the area and base into the area equation {eq}A = \frac{1}{2}bh {/eq} and solve for the height: {eq}9 = \frac{1}{2} 5h {/eq}
- {eq}3.6 in = h {/eq}
- Solve for c using the Pythagorean theorem {eq}c = \sqrt{a^2 + b^2} {/eq}: {eq}c = \sqrt{3.6^2 + 5^2} {/eq}
- {eq}c = 6.2 in {/eq}
- Now that all the sides are found, plug them into the perimeter formula {eq}P = a + b + c {/eq} and solve for the perimeter: {eq}P = 3.6 + 5 + 6.2 {/eq}
