Problem 10 Sketch and label the figure. Mar... [FREE SOLUTION] (2024)

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A rectangle is a four-sided polygon where every interior angle is a right angle (90 degrees). This means all opposite sides are equal in length. Since opposite sides are parallel, you will often encounter properties like:

• The perimeter of a rectangle is calculated as: \ P = 2(l + w) \ where \( l \) is the length and \( w \) is the width.
• The area of a rectangle is given by \ A = l \times w.

The key feature of a rectangle is its symmetry about its diagonals. Let’s explore this in the next section.

In a rectangle, the diagonals are important lines that connect opposite corners. A remarkable property of the diagonals is that they intersect each other at the center of the rectangle, and they are of equal length. Mathematically, this means:

• The diagonal lengths are given by \ d = \sqrt{l^2 + w^2}
• They bisect each other, meaning each half of the diagonal is equal.

For the rectangle \( RGHT \), the diagonals \( \overline{RH} \) and \( \overline{GT} \), intersect at point \( I \). This point is equidistant from all four corners.

Sketching geometrical figures helps in visualizing and understanding their properties. Here’s how to sketch correctly:
1. Start by accurately drawing the shape. For a rectangle, use a ruler to ensure all sides are straight.
2. Label the vertices as mentioned.

• Draw the diagonals from corner to corner.
• Mark the intersection point and label it clearly.

Refer to your labels multiple times to make sure they're correctly placed. Drawing accurately will help you calculate areas, perimeters, and other properties without errors.