Question

Hexagon ABCDEF shown below was drawn on a grid with unit squares. Each vertex is at the intersection of 2 grid lines. what is the area of the hexagon, in square units?​

Answer 1

Answer:

The answer will be 17.5 sq. units.

Step-by-step explanation:

In the hexagon ABCDEF,

ar(∆AEF) = ar(∆ADE) = ar(∆ACD) = 2(ar(∆ABC))

(since they have equal base and same hieght)

Thus, ar(∆AEF) = 1/2 × AF × AE

= 1/2 × 2 × 5

= 5 square units.

Thus, ar(∆ADE) = 5 sq. units.

ar(∆ACD) = 5 sq. units

and, 2(ar(∆ABC)) = 5 sq. units

ar(∆ABC) = 2.5 sq. units

Now, total area of hexagon equals;

ar(∆AEF) + ar(∆ADE) + ar(∆ACD) ar(∆ABC)

5 + 5 + 5 + 2.5

17.5 sq. units.

That's all.