McGraw Hill Glencoe Algebra 2, 2012
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McGraw Hill Glencoe Algebra 2, 2012 View details
7. Transformations of Quadratic Graphs
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Exercise 66 Page 280

To estimate the area of the floor of the building, let's find the area of the triangle with the given vertices.

Recall that the Area of a Triangle with vertices and is half of the absolute value of the following determinant.
Substitute the given points and use the diagonal rule to find the determinant.
The area of the triangle is half of the absolute value of this determinant. Let's also use the information that on the grid each square measures one square foot.
Since we only know the coordinates of three corners of the building, we can only base our estimate of the floor area on assumption about the shape.
  • If this was a triangular building, the floor area is square feet.
  • If there is also a fourth corner not yet found by the archaeologists, then it is reasonable to estimate the floor area as double the area of the triangle, so square feet.

Alternative Solution

Alternative way of thinking

We can also count squares to find the area of the triangle. After noticing that two of the vertices are on a vertical line, we can extend the triangle to a rectangle.

The area of the rectangle is square units. The area of the triangle is half of this, so square units.