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Perimeter and Area of Similar Figures


Here in below figure, triangle ABC is similar to triangle PQR by SAS congruency as two corresponding sides and angle between them are equal. Any two triangles are said to be similar by SAS stands for Side Angle Side congruency condition and if two sides corresponding to the triangles are equal and angle lying between them are also equal. If this congruency condition exists for triangles then those triangles will be similar to each other and it is represented by the symbol ‘~’. This symbol is substituted between two triangles and they are represented as similar.

ASA stands for Angle Side Angle congruency condition which explains that two triangles will be similar if two angles and one side between those angles will be equal. These angles must be corresponding to each other. Similarly, two triangles are said to be similar if both of them are right angled triangle that is one angle is $90^{\circ}$ and one side is equal in a corresponding manner. AAS stands for angle angle side congruency and according to this congruency condition, two triangles will be similar if two Adjacent Angles and one side are equal to two adjacent angles and one side of another triangle. SSS stands for Side Side Side congruency condition, as the name suggests two triangles are said to be similar by SSS when all three sides of one triangle are equal to all three sides of another triangle.

Perimeter and Area of Similar Figures

Perimeter and Area of Similar Figures Definition

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Perimeter is defined as the total of the peripheries of any figure that is the sum total of all sides of a figure. In other words it  is defined for almost every figure that is triangle, rectangle, square and others. For a Rectangle, a perimeter is determined by sum of all sides. Similarly perimeter of a triangle is determined by the sum of all sides of triangle. Area is termed as total area covered by any figure or  total space covered by any figure is defined as area for that figure.For similar figures these may be equal or may not be equal as similarity is defined in different forms for Triangles. It includes SAS congruency, ASA congruency, RHS congruency, AAS congruency and SSS congruency. Any two triangles are said to be similar if they satisfy the above congruency conditions.

Perimeter and Area of Similar Figures

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Perimeter is measure of outer boundary of any multi - sided plane shape. Area is defined as total space occupied by any 2 –dimensional shape. These shapes are regular figures that we have been discussing so far in our mathematics. Perimeter and area word problems are those problems in which we will find measures and other information of shape being given in form of statements. We need to find useful data from these problems to evaluate Area And Perimeter for shape that has been described. To solve these problems first you require noting all data in numeric way. Next step would be using formulae that have been defined for various shapes. 


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Let us see some examples of word problems solving for area and perimeter.
Example 1: 

Length of one side of a Square is 10 units. What will be the area and perimeter of square?


About square we know that all of its sides are of equal length. It means all sides will have same measure s = 10.

Area of a square is given as $A = s \times s = 10 \times 10 = 10 unit^{2}$,


Perimeter is given as: $P = 4s = 4 \times 10 = 40$ units.
Example 2:

Let us now make the problem more complicated by taking a small square inside bigger one. Length of one side of small square is 4 units and that of bigger one is 8 units. Calculate the area and perimeter for both squares?


Figure for problem can be drawn as:

Perimeter and Area of Similar Figures Examples

Area of small square can be calculated as $a\ =\ 4\ \times\ 4\ =\ 16\ units^{2}$,

To calculate area of bigger square we need to subtract space occupied by smaller square in bigger one. So, area for bigger square can be calculated as: $8\ \times\ 8\ –\ 16\ =\ 64\ –\ 16\ =\ 48 units^{2}$.

Perimeter Inner: $4\ \times\ 4\ =\ 16\ units$.

Perimeter Outer: $4\ \times\ 8\ =\ 32\ units$.