Question

What is the area of triangle ABC?

3 square units
7 square units
11 square units
15 square units

Answer 1

The area of triangle is 7 square units, which is mentioned in option B. It is obtained from the given diagram.

Explanation:

The given is,

For above question diagram is missing, so i attach the diagram.

Step:1

Formula for area of triangle from the coordinates,

`A =(1)/(2) [ x_(1)(y_(2) -y_(3))+x_(2) (y_(3)-y_(1) )+x_(3)(y_(1) - y_(2) )]`.............(1)

Where,

`(x_(1) ,y_(1) ),(x_(2) ,y_(2) ), (x_(3) ,y_(3) )` are coordinates

From the given,

A ( 1, 1 ) -
`(x_(1) , y_(1) )`

B ( 4, 0 ) -
`(x_(2) , y_(2) )`

C ( 3, 5 ) -
`(x_(3) , y_(3) )`

Equation (1) becomes,

Area,
`A = (1)/(2) [1(0-5)+4(5-1)+3(1-0)]`

`= (1)/(2) [1(-5)+4(4)+3(1)]`

`= (1)/(2) [ -5 +16 + 3]`

`= (1)/(2) (14)`

= 7

Area of triangle, A = 7 square units

Result:

The area of triangle is 7 square units, which is mentioned in option B. It is obtained from the given diagram.