Question

What is the area of the triangle?

Answer 1

9514 1404 393

Answer:

  7 square units

Step-by-step explanation:

There are several ways the area of triangle EBD can be found.

• find the lengths EB, BD, DE and use Heron's formula (messy due to roots of roots being involved).
• define point G at the lower left corner and subtract the areas of ∆DEG and BCD from trapezoid BCGE.
• figure the area from the coordinates of the vertices.
• use Pick's theorem and count the dots.

We choose the latter.

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Pick's theorem says the area of a polygon can be found as ...

  A = i + b/2 -1

where i is the number of grid intersection points interior to the polygon, b is the number of grid points intersected by the border.

The attached figure shows the lines EB, BD, and DE intersect one point in addition to the vertices. So, b=4. A count of the red dots reveals 6 interior points (i=6). So, the area is ...

  A = 6 + (4/2) -1 = 7

The area of ∆EBD is 7 square units.