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#### Find The Area Of An Isosceles Triangle

Referencing Styles : MLA | Pages : 1

Geometry has the application of the isosceles triangle. The isosceles triangle is the type of a triangle, which have the two sides with equal lengths. Any triangle that have the two sides whose lengths are exactly same to each other are referred as the isosceles triangle. There is a special case that includes the term equilateral triangle. There are examples of the isosceles triangles and they are golden triangle, bipyramid’s faces, specific Catalan solids and isosceles right triangle. The first study of the isosceles triangles can be found in the mathematics of the ancient Egypt and the mathematics of the Babylon. The application of the isosceles triangles used to be used as the form of decoration even in earlier times than the periods mentioned above. The application of the isosceles can be found in the design and architecture of the buildings as gables and pediments. The two of three sides of isosceles triangle is known as the legs and the other side or the third side is known as the base. There are other dimensions in the triangle including area, perimeter and height, which can be figured out by calculating with the help of simple formulas. All of the isosceles triangle include the symmetry axis which is placed along the base’s perpendicular bisector. There are two acute angles present in the two opposite side of the legs. Hence, the classification of the isosceles triangle is completely dependent on the angles that are present between the legs of the triangle.

The triangle that have two equal sides is isosceles triangle and the famous mathematician Euclid defined this. However, the modern mathematics defines the isosceles triangle as a triangle, which includes at least two sides that are equal. The primary difference between these two definitions is modern mathematics refers the isosceles triangle’s special case as the equilateral triangles. When a triangle do not have the sides with the equal lengths then that means the triangle is not a isosceles and they defined by the term scalene. The word isosceles is the composition of two words. The origin of the isosceles triangle originated from the words ‘isos’ and ‘skelos’. These two words are Greek words. The meaning of the word ‘isos’ means something, which is equal to some other thing. The meaning of the word ‘skelos’ is legs. There other instances where is the same words have been used such as in the case of isosceles trapezoids and isosceles sets. Here the trapezoids consists of two sides, which are equal. Vertex angle is the term that is used to define the angles between the legs. The term Base angles are used to define the angles, which have base included. Apex is the term that is used to describe the vertex that is present at the opposite side of the base. In the case of equilateral triangles, all the sides are of the equal lengths hence there is no way to determine which sides are the legs and which side is the base. Hence, any side of the equilateral triangle can be referred as the base of the triangle.

Finding the area of an isosceles triangle is very easy method. We need the value of height and the value of base of the triangle in order to calculate the area of that isosceles triangle. The formula to find the area of the triangle is-

A = ½bh

There is a simple and normal relation present between the shapes of a parallelogram and the isosceles triangle. If we cut a parallelogram in half diagonally, then it creates two triangles whose area are the same. In the same way, two triangles can be joined together to form a parallelogram. Hence, the above formula satisfies that the area of parallelogram is A = bh. Thus, the area of an isosceles triangle is the A = ½bh.

Let us assume, we have isosceles triangle with the value of the base is 6 cm and the value of the two sides are the 5 cm. Then we have to draw a line from the top vertex of the isosceles triangle to the base of the same. We have to make sure that the line hits the base of the triangle exactly at right angle. This drawn line is the required height of the isosceles triangle. In case of isosceles triangle, the drawn line always hits at the middle of the base. Now we have two short sides and a long side in the triangle. The base is now at the length of b/2, the drawn line is h, and the longer side is the s. Now we have to apply the theorem of Pythagoras which is in the form of a2 + b2 = c2. So here the value of the a2 is equal to the (b/2)2 and the value of b2 is the height, which is h2, and finally the value of c2 is s2. As we do not know the value of h yet, thus, we have to rearrange the equation in such a way so that we can identify the value of h. The value (b/2)2 has to be subtracted from the value s2 and the h2 would be on the other side of the equal sign. After putting the value 5 at the place of s and 3 at the place of (b/2) we get the value of h as 4cm. Hence, the height is 4 cm. Now we have the value of height as well as the value of the base. So, now if we put the values of height and base in the above-mentioned equation for finding the Area of isosceles triangle, the required value of the Area can be found. Let us put the value in the right place –

A = ½bh

A = ½(6cm) (4cm)

A = 12cm2.

Hence, it can be seen that the required Area of the isosceles triangle is 12 cm per square unit or 12 cm2. The observation from the above calculation is that the result of the calculation to find the Area should always be written in terms of square units.

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