Скачать с ютуб Why area of the triangle is 1/2 x base x height? - Part 2 | English в хорошем качестве

Why area of the triangle is 1/2 x base x height? - Part 2 | English

There are three types of triangles based on their angles: Right angle triangle, acute triangle and obtuse triangle. How can we prove that the area of these triangles is also given by the formula: ½ x height x base? Let us prove this formula by visualizing it through an experimental activity. Hello friends, In this video we will be discussing what will happen to the area of the triangle if we have different types of triangles based on their angles? How can we prove the area of these triangles can also be given by the formula: ½ height x base? For this we will need three different types of triangles Right angled triangle- one of the angle is 90° Acute angled triangle- all the angles are less than 90° Obtuse angled triangle - one of the angle is greater than 90° Let us look at the right angled triangle, Mark the base and the height of the triangle, Fold the triangle along the height to get a line parallel to the base at half of the height. Draw the line with a marker. Cut along this line with a scissors to get two parts, one smaller triangle and one trapezium. Arrange the smaller triangle along the trapezium to form a complete rectangle. This rectangle formed has breadth same as the base of the triangle and length as half of the height of the triangle. Since this is made from the pieces of the triangle, it will have the same area: Area of the right angled triangle = Area of the rectangle formed = length x breadth = ½ height x base (length and breadth as compared to the triangle) Thus we have found that Area of the right angled triangle is also equal to ½ height x base Now lets’ see whether this works for acute angled triangle too! Mark base of the triangle and draw a perpendicular to mark the height of the triangle. Now fold the triangle to get a parallel line to the base at exactly half the height as shown in the video. Draw the line with a marker. Cut the half part similar to the earlier case. Now fold the small triangular piece along the height and cut it into two smaller triangles. You will get three pieces: two triangles and one trapezium. Arrange them so that we get a complete rectangle which has breadth same as the base of the triangle and length as half of the height of the triangle. Thus just like the earlier case we can prove that, Area of the right angled triangle = Area of the rectangle formed = ½ height x base Now lets’ do this for obtuse angled triangle too! If we take the longer side as base, we can just prove it similar to the acute angled triangle. Its’ easy, isn’t it? Try for yourself. Now let us consider for the smaller side as base. Mark b as the base, draw the perpendicular from the base of the triangle. Take help of a stick or scale to get the height. Take half of the height and draw a line as shown in the video. Now cut across this line and arrange the triangle along the figure to get a parallelogram. Now cut the smaller triangle and arrange it along the parallelogram to form a rectangle. So we have transformed the obtuse angled triangle into a rectangle whose breadth same as the base of the triangle and length is half of the height of the triangle. Thus just like the case 1 we can prove that the area of the obtuse angled triangle is same as this rectangle which is ½ height x base. Thus in all the above three cases we have found that Area of the triangle = ½ height x base Team: Ashok Rupner, Chaitanya Mungi, Shanti Pise, Neha Apte Music: Dr. Manasi Kulkarni