Math, asked by pareekgautam1014, 1 year ago

Find the area of triangle PQR whose vertices areP(-5,7) ,Q(-4,-5) and R(4,5)

Answers

Answered by amitnrw
3

Given : A triangle PQR whose vertices are P(-5,7) ,Q(-4,-5) and R(4,5)

To find : Area of Triangle PQR

Solution:

P = (-5 , 7)

Q = ( -4 , - 5)

R = ( 4 , 5)

Area of Triangle PQR

= (1/2) |  -5(-5 - 5) -4(5 - 7)  + 4(7 -(-5))|

= (1/2) | 50 + 8 + 48 |

= (1/2) | 106 |

= 106/2

= 53

Area of Triangle PQR = 53 sq units

Learn more:

Find the area of the triangle whose vertices are :(-4,6) (20,8) (9,10 ...

https://brainly.in/question/12361320

find the area of triangle having vertices at (8,1) ,(1,-4),(4,-5)

https://brainly.in/question/12350448

find the area of triangle having vertices at (8,1) ,(1,-4),(4,-5)

https://brainly.in/question/12350448

Answered by MananyaMuhury
1

Answer and Step-by-step Explanation:

Given:

✰ Point P( -5, 7 )  

✰ Point Q( -4, -5 )  

✰ Point R ( 4, 5 )

To find:

✠ The area of triangle PQR

Solution:

Consider,  

In point P( -5, 7 )

✫ -5 = x₁  

✫ 7 = y₁  

In point Q( -4, -5 )  

✫ -4 = x₂  

✫ -5 = y₂  

In point R ( 4, 5 )

✫ 4 = x₃

✫ 5 = y₃

Now,

Area of ∆PQR = 1/2[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)]

Area of ∆PQR = 1/2 [ -5( -5 - 5 ) -4( 5 - 7 ) +4( 7 + 5 )]

Area of ∆PQR = 1/2 [ ( 25 + 25 ) + ( - 20 + 28 ) + ( 28 + 20 ) ]

Area of ∆PQR = 1/2 [ 50 + 8 + 48 ]

Area of ∆PQR = 1/2 [ 58 + 48 ]

Area of ∆PQR = 1/2 [ 58 + 48 ]

Area of ∆PQR = 1/2 [ 106 ]

Area of ∆PQR = 1/2 × 106

Area of ∆PQR = 53 sq.unit

∴ The ∆ of triangle PQR = 53 sq.unit

 

Signs:

+ + = +

- - = +

- + = -

+ - = -

══════════════════════

Hope it helps you!(●ˇ∀ˇ●)

Similar questions