Question

Find the area of △DEF with vertices D(5, 16), E(12, 6), and F(4, 6). The area of △DEF is ____ square units.

a) 30
b) 36
c) 40
d) 45

Answer 1

The area of triangle DEF with given vertices is found using the coordinates area formula and is 40 square units, corresponding to option c).

Step-by-step explanation:

To find the area of triangle DEF with vertices D(5, 16), E(12, 6), and F(4, 6), we can use the formula for the area of a triangle with three coordinates (x1,y1), (x2,y2), and (x3,y3) which is given by:

Area = \(\frac{1}{2}| x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) |\).

Substituting the given coordinates:

\(\frac{1}{2}|5(6 - 6) + 12(6 - 16) + 4(16 - 6)|\)

= \(\frac{1}{2}| 0 + 12(-10) + 4(10) |\)

= \(\frac{1}{2}| -120 + 40 |\)

\(\frac{1}{2}| -80 |\) = 40 square units.

So, the area of triangle DEF is 40 square units, which corresponds to option c).