Question

if I have a rectangle and I want to obtain 5 triangles from it how many times I have to fold it​

Answer 1

Answer:

Solved Example

Let us take an example of a rectangle having length = 8cm and width = 5cm.

So, Area of rectangle = Length x width

= 8cm x 5 cm

= 40 cm2 ……………(i)

Now divide the rectangle, along its diagonal, into two triangles. The two triangles obtained are both right-angled triangles.

Height of the right triangles = 5cm each

Base of the right triangle = 8cm each

Now, by the formula of area of triangle we know;

Area of Triangle-1 = ½ (base) x (height)

= ½ (8cm) x (5cm)

= 20cm2

The area of another triangle will also be the same, since height and base values are the same. Therefore,

Area of Triangle-2 = 20cm2

Now if we add, the areas of the two triangles, we get;

Area of (Triangle-1 and Triangle-2) = 20cm2 + 20cm2

Area = 40 sq.cm ………..(ii)

By equation (i) and (ii) we can say that;

Area of rectangle = Sum of Area of triangles as parts of rectangle

By this we can also conclude that;

Area of triangle as parts of rectangle = ½ Area of rectangle

= ½ (Length x Width)

Triangles as parts of Square

Here also, the same theory is applicable to what we have understood for triangles as parts of rectangles.

A square has all its sides equal. Suppose we have a square with sides equal to ‘a’. Then by the formula of area of square;

Area (Square) = a x a = a2 ………..(i)

Now, divide the square into two parts by cutting it diagonally. Again we got two triangles that superimposed on each other.

Since, the square has all its sides equal, therefore, on dividing it diagonally, we will get two right-isosceles triangles, having base and height equal to ‘a’.

Base = a unit

Height = a unit

Area of Triangle-1 = ½ a x a = a2/2

Area of Triangle-2 = ½ a x a = a2/2

By adding the areas of two triangles, we get;

Sum of areas of two triangles = a2/2 + a2/2 = 2(a2/2) = a2 ……………(ii)

Therefore, by equation (i) and (ii), we get;

Area of square = Sum of Area of triangles as parts of square

We can also conclude that:

Area of each triangle as parts of square = ¼ (Area of square)

In geometry, we have learned different shapes and sizes that are used to define the shapes in the real world. By learning the relationship between two or more shapes, we can easily determine the required dimensions or area.