What is the area of a rectangle with vertices at (1, 1), (1, 4), (5, 1), and (5,

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Question: What is the area of a rectangle with vertices at (1, 1), (1, 4), (5, 1), and (5, 4)?

Options:

Correct Answer: 12

Solution:

Length = 5 - 1 = 4, Width = 4 - 1 = 3. Area = length * width = 4 * 3 = 12.

What is the area of a rectangle with vertices at (1, 1), (1, 4), (5, 1), and (5, 4)?

What is the area of a rectangle with vertices at (1, 1), (1, 4), (5, 1), and (5, 4)?

Step 1: Identify the coordinates of the vertices of the rectangle: (1, 1), (1, 4), (5, 1), and (5, 4).
Step 2: Determine the length of the rectangle. The length is the distance between the x-coordinates of the points (1, 1) and (5, 1). Calculate it as 5 - 1 = 4.
Step 3: Determine the width of the rectangle. The width is the distance between the y-coordinates of the points (1, 1) and (1, 4). Calculate it as 4 - 1 = 3.
Step 4: Calculate the area of the rectangle using the formula: Area = length * width.
Step 5: Substitute the values: Area = 4 * 3.
Step 6: Calculate the final area: Area = 12.

Geometry of Rectangles – Understanding the properties of rectangles, including how to calculate length and width from given vertices.
Coordinate Geometry – Using coordinates to determine the dimensions of geometric shapes.
Area Calculation – Applying the formula for the area of a rectangle (Area = length * width).