Mrs. Thomas wants to put a table in the corner of a room. She considers the measurements of these tables. Table 1 length: 1.5 fe
et width: 2.4 feet diagonal: 3.0 feet Table 3 length: 2.4 feet width: 3.2 feet diagonal: 4.0 feet Table 2 length: 3.2 feet width: 2.8 feet diagonal: 4.0 feet Table 4 length: 2.6 feet width: 1.8 feet diagonal: 3.0 feet The walls forming the corner meet at a 90° angle. Which table will fit snugly in the corner? O Table 1 O Table 2 O Table 3 O Table 4
2 answers:
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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.
