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PLEASE HELP URGENT

If the area of the rectangle is 36 square units, what is the eare of the inscribed triangle?

PLEASE HELP URGENT If the area of the rectangle is 36 square units, what is the eare-example-1
User Eli Waxman
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1 Answer

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Answer:

14.5 square units

Explanation:

You want the area of the triangle inscribed in the 4×9 rectangle shown.

Pick's theorem

Pick's theorem tells you the area can be found using the formula ...

A = i +b/2 -1

where i is the number of interior grid points, and b is the number of grid points on the boundary. This theorem applies when the vertices of a polygon are at grid intersections.

The first attachment shows there are 14 interior points, and 3 boundary points. Then the area is ...

A = 14 + 3/2 -1 = 14 1/2 . . . . square units

The area of the triangle is 14.5 square units.

Determinants

The area of a triangle can also be found from the determinant of a matrix of its vertex coordinates. The second attachment shows the area computed for vertex coordinates A(0, 4), C(7, 0) and B(9, 3).

The area of the triangle is 14.5 square units.

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Additional comment

The area can also be found by subtracting the areas of the three lightly-shaded triangles from that of the enclosing rectangle. The same result is obtained for the area of the inscribed triangle.

The area value shown in the first attachment is provided by the geometry app used to draw the triangle.

We find the least work is involved in counting grid points, which can be done using the given drawing.

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PLEASE HELP URGENT If the area of the rectangle is 36 square units, what is the eare-example-1
PLEASE HELP URGENT If the area of the rectangle is 36 square units, what is the eare-example-2
User Jet Blue
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7.6k points