Question

Find the area of ​​the vertex triangle using the determinant:(11,8),(3,2),(8,12)
________________________________

Answer with proper explanation.

The correct respondent will get 100+ thanks.


Don't spam.


→ Expecting answer from :

★ Moderators
★ Brainly stars and teacher
★ Others best users ​
​

Answer 1

answer :- 30

Step-by-step explanation:

a (11,8) b (3,2) c (8,12)

area of triangle = 1/2 | x1 (y2-y3) +x2 ( y3-y1 ) + x3 ( y1- y2

$\frac{1}{2}$

Answer 2

Answer : 25

Ok, so lets start

So lets assume

Vertex A of triangle is (11,8)

Vertex B of triangle is (3,2)

Vertex C of triangle is (8,12)

(Just assume vertices are like that).

so, you'll need to use the coordinate geometry formula:

area = | {Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By) }/2 |

Ax and Ay are the x and y coordinates for the vertex of A. The same applies for the x and y notations of the B and C vertices.

$\frac{ 11(2 - 12) + 3(12 - 8) + 8(8 - 2)}{2}$

$= \frac{ - 110 + 12 + 48}{2}$

$\frac{ - 50}{2} = - 25$

remove negative sign form -25.

hence, area = 25.

Or another way is,

Consider the ∆ ABC:

Given in the figure

one by one find the length of sides and calculate area using herons formula. (find the sides using Pythagoras theorem).

as A = (11,8)

B = (3,2)

C = (8,12)

length of AB = √ (| Ax - Bx |)² + (| Ay - By|)²

length of BC = √ (| Bx - Cx |)² + (| By - Cy |)²

length of AC = √ (| Ax - Cx |)² + (| Ay - By |)²

$s = \frac{AB + BC + AC}{2}$

$area \: = \sqrt{s(s - a)(s - b)(s - c)}$

so let's try:

$AB = \sqrt{( |11 - 3| )^{2} + ( |8 - 2| )^{2} } \\ = \sqrt{{8}^{2} + {6}^{2} } \\ = \sqrt{64 + 36} \\ = \sqrt{100} = 10$

$BC = \sqrt{( |3 - 8| )^{2} + ( |2 - 12|) ^{2} } \\ = \sqrt{ {5}^{2} + {10}^{2} } \\ = \sqrt{25 + 100} \\ = \sqrt{125} = 5 \sqrt{5}$

$AC = \sqrt{ {( |11 - 8| )}^{2} + {( |8 - 12| )}^{2} } \\ = \sqrt{ {3}^{2} + {4}^{2} } \\ = \sqrt{9 + 16} \\ = \sqrt{25} = 5$

now,

$s = \frac{10 + 5 \sqrt{5} + 5}{2} \\ = \frac{15+5\sqrt{5}}{2}$

$Area = \sqrt{ \frac{ 15+5 \sqrt{ 5 } }{ 2 } ( \frac{ 15+5 \sqrt{ 5 } }{ 2 } -10)( \frac{ 15+5 \sqrt{ 5 } }{ 2 } -5 \sqrt{ 5 } )( \frac{ 15+5 \sqrt{ 5 } }{ 2 } -5) }$

$= \sqrt{625} = 25$

and...

hooray!

same answer 25 using both methods.