Question

What is the area of a trapezoid with coordinates D 4,3 E 4,0 F 2,1 and G 2,3

Answer 1

5 square units.

Explanation:

See the attached graph where D, E, F, and G points are plotted.

So, in trapezium DEFG, the parallel sides are GF and DE.

Now, it is clear from the graph that, the length of segment GF = (3 - 1) = 2 units and the length of line segment DE = (3 - 0) = 3 units.

Now, the altitude of the trapezium is GD with length (4 - 2) = 2 units.

Therefore, the area of the trapezium will be given by

`A = (1)/(2) * (GF + DE) * GD`

⇒
`A = (1)/(2) * (3 + 2) * 2 = 5` square units. (Answer)