25.5 Perimeter and Area on the Coordinate Place

Front

What is the formula for calculating the area of a quadrilateral given its vertices?

Back

The area can be calculated using the shoelace formula: Area = 1/2 | Σ (x_i * y_(i+1) - y_i * x_(i+1)) |, where (x_i, y_i) are the coordinates of the vertices.

Front

How do you calculate the perimeter of a polygon given its vertices?

Back

The perimeter is calculated by summing the lengths of all the sides. For vertices (x1, y1), (x2, y2), ..., (xn, yn), the perimeter P = Σ √((x_(i+1) - x_i)² + (y_(i+1) - y_i)²) for i from 1 to n, with (x_(n+1), y_(n+1)) = (x1, y1).

Front

What is the distance formula used to find the length of a side between two points (x1, y1) and (x2, y2)?

Back

The distance d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the significance of rounding in perimeter calculations?

Back

Rounding is important to provide a practical answer, especially in real-world applications where exact measurements may not be possible.

Front

How do you find the area of a triangle given its vertices?

Back

The area can be calculated using the formula: Area = 1/2 | x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) |.

Front

What is the formula for the perimeter of a triangle with vertices A(x1, y1), B(x2, y2), C(x3, y3)?

Back

Perimeter = AB + BC + CA = √((x2 - x1)² + (y2 - y1)²) + √((x3 - x2)² + (y3 - y2)²) + √((x1 - x3)² + (y1 - y3)²).

Front

What is the shoelace formula used for?

Back

The shoelace formula is used to calculate the area of a polygon when the coordinates of its vertices are known.

Front

What is the difference between area and perimeter?

Back

Area measures the space inside a shape, while perimeter measures the distance around a shape.

Front

How do you determine the coordinates of the centroid of a triangle?

Back

The centroid (G) can be found using the formula: G = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).

Front

What is the relationship between the coordinates of a point and its distance from the origin?

Back

The distance from the origin (0,0) to a point (x,y) is given by d = √(x² + y²).