Question

In the accompanying figure, triangle ABC has coordinates A(0,3), B(7,3), C(7,7). What is the area of triangle ABC in square units?

Answer 1

We know area of triangle =
`(1)/(2) * base * height`

In triangle ABC , AB is the base and BC is the height

Now we find the distance between A and B

Distance formula is
`√((x_2-x_1)^2 + (y_2-y_1)^2)`

A(0,3), B(7,3)

Distance AB =
`√((7-0)^2 + (3-3)^2)`

=
`√((7)^2 )` = 7

B(7,3), C(7,7)

Distance BC =
`√((7-7)^2 + (7-3)^2)`

=
`√((4)^2 )` = 4

area of triangle =
`(1)/(2) * base * height`

area of triangle =
`(1)/(2) * AB * BC`

=
`(1)/(2) * 7 * 4` = 14
`units ^2`