What is Brahmaputra formula?

What is Brahmaputra formula?

S = \sqrt{(s – a)(s – b)(s – c)(s – d)}, where s is the semiperimeter of the quadrilateral: s = (a + b + c + d)/2. It is interesting to note that Heron’s formula is an easy consequence of Brahmagupta’s.

How do you prove brahmagupta’s Theorem?

Hence, AFM is an isosceles triangle, and thus the sides AF and FM are equal. The proof that FD = FM goes similarly: the angles FDM, BCM, BME and DMF are all equal, so DFM is an isosceles triangle, so FD = FM. It follows that AF = FD, as the theorem claims.

What is Thales formula?

0 = (A − B) · (B − C) = (A − B) · (B + A) = |A|2 − |B|2. Hence: |A| = |B|. This means that A and B are equidistant from the origin, i.e. from the center of M.

What is Heron’s Formula 10?

Heron’s formula is a formula to calculate the area of triangles, given the three sides of the triangle. This formula is also used to find the area of the quadrilateral, by dividing the quadrilateral into two triangles, along its diagonal.

What is the formula of cyclic quadrilateral?

In a cyclic quadrilateral, p × q = sum of product of opposite sides, where p and q are the diagonals. The sum of a pair of opposite angles is 180° (supplementary). Let ∠A, ∠B, ∠C, and ∠D be the four angles of an inscribed quadrilateral. Then, ∠A+∠C=180° and ∠B+∠D=180°.

What is Brahmagupta’s formula?

Brahmagupta’s Formula and Theorem Brahmagupta – an Indian mathematician who worked in the 7th century – left (among many other discoveries) a generalization of Heron’s formula: The area $S$ of a cyclic quadrilateralwith sides $a, b, c, d$ is given by

How to find the area of a quadrilateral using Brahmagupta’s formula?

1. If ABCD is a quadrilateral with sides of length a, b, c, and d, such that ABCD is both cyclic and has a circle inscribed in it, then use Brahmagupta’s formula to show that the area of the quadrilateral is 2. Consider Brahmagupta’s formula as one side, say the one of length d wnlog, varies and approaches zero in length.

How do you find the radius of a cylinder?

Let V be the volume of the cylinder, r the radius of the base, and h the height. Then, recall that the volume is equal to pi*r^2*h. That is: V = pi* (r^2)*h. We can solve this equation for r in order to calculate radius when given volume and height. We’ll go over that process in the video, but what we end up with is r = sqrt (V/ (pi*h)).

What is the difference between Brahmagupta’s and Heron’s formula?

It is interesting to note that Heron’s formula is an easy consequence of Brahmagupta’s. To see that suffice it to let one of the sides of the quadrilateral vanish. On the other hand, Heron’s formula serves an essential ingredient of the proof of Brahmagupta’s formula found in the classic textby Roger Johnson.