Question

Write an activity to find the are of a triangle by applying heron's formula using graph paper and verifying for the same.​

Answer 1

Explanation given below

Step-by-step explanation:

The formula given by Heron about the area of a triangle, is also known as Hero’s formula. It is stated as:

$\text { Area of a triangle }=\sqrt{s(s-a)(s-b)(s-c)}$

where a, b and c are the sides of the triangle, and s = semi-perimeter, i.e., half the perimeter of the triangle = $\frac{a+b+c}{2}$

Activity: find the are of a triangle whose vertices have coordinates (3,5),(6,-5), and (-4,10)

Graph attached below

Distance Formula calculations:

$\begin{aligned}&\sqrt{(3-6)^{2}+(5--5)^{2}}=\sqrt{109}\\&\sqrt{(3--4)^{2}+(5-10)^{2}}=\sqrt{74}\\&\sqrt{(6--4)^{2}+(-5-10)^{2}}=\sqrt{325}\end{aligned}$

$\begin{aligned}&s=\frac{\sqrt{109}+\sqrt{74}+\sqrt{325}}{2}\\&\text { Area }=\sqrt{(5)(5-\sqrt{109})(5-\sqrt{74})(6-\sqrt{325})}\\\end{aligned}$

To learn more

i)Sides of a triangular field are 15m, 16m, and 17m. With the three corners of the field a cow, a buffalo and a horse are tied separately with ropes and length 7meach to graze in the field. Find the area of the field which cannot be grazed by the three animals.

https://brainly.in/question/1026183

ii) What are the uses of heron's formula in daily life?

https://brainly.in/question/786950