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Area and Perimeter of Similar Polygons Loading... Found a content error? Notes/Highlights
Image AttributionsShowHide DetailsI must admit that when I saw the request on the calculator creation/2658/, which sounded like "calculate area by perimeter". I was a little surprised because it looked somewhat surreal. Although, after some search on the Internet, I realized that the request just not complete, and often goes like this: "Calculate the area of a rectangle if its perimeter is equal to X and it is known that ..." - and there are different things that may be known. These things lead us to a solution—for example, the length of one of the sides or the aspect ratio. The calculator below calculates the rectangle area, depending on what else is known apart from the perimeter. I dedicate it to all students. Rectangle area calculation by perimeterone side is longer than the other by one side is shorter than the other by Calculation precision Digits after the decimal point: 2 Created by Krishna Nelaturu Reviewed by Anna Szczepanek, PhD and Steven Wooding Last updated: Jul 15, 2022 This similar triangles calculator is here to help you find a similar triangle by scaling a known triangle. You can also use this calculator to find the missing length of a similar triangle! Stick around and scroll through this article as we discuss the laws of similar triangles and learn some fundamentals:
What are similar triangles?Two triangles are similar if their corresponding sides are in the same ratio, which means that one triangle is a scaled version of the other. Naturally, the corresponding angles of similar triangles are equal. For example, consider the following two triangles: Notice that the corresponding sides are in proportion: DEAB =EFBC=DFAC=2\frac{\text{DE}}{\text{AB}} = \frac{\text{EF}}{\text{BC}} =\frac{\text{DF}}{\text{AC}} = 2 Therefore, we can say △ABC \triangle \text{ABC} ∼\sim △DEF\triangle \text{DEF}. Here the symbol ∼\sim indicates that the triangles are similar. We term the proportion of similarity as the scale factor (k)(k). In the example above, the scale factor k=2k = 2. If you need help finding ratios, use our ratio calculator. Finding similar triangles: Law of similar trianglesWe know that two triangles are similar if either of the following is true:
From this, we can derive specific rules to determine whether any two triangles are similar:
We can express this using a similar triangle formula: DEAB=EFBC=DFAC=k\qquad \frac{\text{DE}}{\text{AB}} = \frac{\text{EF}}{\text{BC}} =\frac{\text{DF}}{\text{AC}} = k where kk is the scale factor.
The triangles in the image above are similar if: DEAB=DFAC=k ,and∠BAC=∠EDF\qquad \begin{align*} &\frac{\text{DE}}{\text{AB}} = \frac{\text{DF}}{\text{AC}} = k, \text{and}\\\\ & \angle\text{BAC} = \angle\text{EDF} \end{align*} This rule is handy in cases like in the image below, where the triangles share an angle: You can do many things knowing just the Side-Angle-Side of a triangle. Learn more using our SAS triangle calculator.
The triangles in the image above are similar if: ∠BAC=∠EDF, ∠ABC=∠DEF, and DEAB=k\qquad \begin{align*} & \angle\text{BAC} = \angle\text{EDF}, \\ & \angle\text{ABC} = \angle\text{DEF}, \text{ and}\\\\ &\frac{\text{DE}}{\text{AB}} = k \end{align*} You can find the third angle if you know any two angles in a triangle using our triangle angle calculator. We know that if any two corresponding angles in the triangles are equal, the triangles are similar, meaning that in the ASA congruence rule, we don't need to know the side so long as the angles are known. However, without the sides, we cannot determine the scale factor kk. How do you find the missing side of a similar triangle?To find the missing side of a triangle using the corresponding side of a similar triangle, follow these steps:
For example, consider the following two similar triangles. To find the missing side, we first start by calculating their scale factor. k=DEAB=84=2k = \frac{\text{DE}}{\text{AB}} = \frac{8}{4} = 2 Next, we use the scale factor relation between the missing side AC and its corresponding side DF: DFAC=k=2AC=DF2=62AC=3\begin{align*} \frac{\text{DF}}{\text{AC}} &= k=2\\[1em] \text{AC} &= \frac{\text{DF}}{2} = \frac{6}{2}\\[1em] \text{AC} &= 3 \end{align*} How do you find the area of a similar triangle?To find the area of a triangle A1 from the area of its similar triangle A2, follow these steps:
How to use this similar triangles calculatorNow that you've learned how to find the length of a similar triangle, the similar triangles formula, and more, you can quickly figure out how this similar triangles calculator works. To check whether two known triangles are similar, use this calculator as follows:
To use this calculator to solve for the side or perimeter of similar triangles, follow these steps:
FAQAre all equilateral triangles similar?Yes, if the corresponding angles of two triangles are equal, the triangles are similar. Since every angle in an equilateral triangle is equal to Find the scale factor of similar triangles whose areas are 10 cm² and 20 cm²?1.414. To determine this scale factor based on the two areas, follow these steps:
30 60 90 triangle45 45 90 triangleArea of a right triangle… 15 more How do you find the ratio of area of similar figures?To find the area ratios, raise the side length ratio to the second power. This applies because area is a square or two-dimensional property. We can use this idea of similarity and apply it to area.
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Ratio of perimeter and area of similar figures calculator
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