Answer:
Therefore, the area of the triangle with vertices at A(2, 2), B(4, 5), and C(7, 5) is approximately 4.5, to the nearest tenth.
Explanation:
To find the area of a triangle with vertices at A(2, 2), B(4, 5), and C(7, 5), you can use the Shoelace Theorem.
The Shoelace Theorem states that the area of a polygon with vertices (x1, y1), (x2, y2), ..., (xn, yn) is given by the following formula:
A = 1/2 * |(x1y2 + x2y3 + ... + xn-1yn + xny1) - (y1x2 + y2x3 + ... + yn-1xn + ynx1)|
To apply the Shoelace Theorem to a triangle with vertices at A(2, 2), B(4, 5), and C(7, 5), you can plug in the coordinates of these vertices into the formula:
A = 1/2 * |(25 + 45 + 72) - (24 + 57 + 52)|
= 1/2 * |(10 + 20 + 14) - (8 + 35 + 10)|
= 1/2 * |44 - 53|
= 1/2 * |-9|
= 1/2 * 9
= 4.5