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Magazine Chapter 1: Problem 1
Draw and label two rectangles and one parallelogram, each having an area of 12 square feet.
Short Answer
Expert verified
Rectangles: 4x3 and 6x2 feet; Parallelogram: base 4, height 3 feet.
Step by step solution
01
Understanding Area Formula for Rectangles
The area of a rectangle is calculated using the formula \( A = l \times w \) where \( l \) is the length and \( w \) is the width. Our rectangle must have an area of 12 square feet.
02
Determine Dimensions for Rectangles
Let's choose simple dimensions for two rectangles. For the first rectangle, let \( l = 4 \) feet and \( w = 3 \) feet, because \( 4 \times 3 = 12 \). For the second rectangle, we can use \( l = 6 \) feet and \( w = 2 \) feet, so \( 6 \times 2 = 12 \).
03
Draw and Label Rectangles
Draw two rectangles, one with dimensions 4 feet by 3 feet and label it 'Rectangle 1', and another with dimensions 6 feet by 2 feet and label it 'Rectangle 2'. Ensure each has an area of 12 square feet.
04
Understanding Area Formula for Parallelogram
The area of a parallelogram is given by \( A = b \times h \), where \( b \) is the base and \( h \) is the height. Our parallelogram must also have an area of 12 square feet.
05
Determine Dimensions for Parallelogram
Let's choose dimensions where \( b = 4 \) feet and \( h = 3 \) feet. This satisfies the area calculation because \( 4 \times 3 = 12 \).
06
Draw and Label Parallelogram
Draw a parallelogram with a base of 4 feet and a height of 3 feet. Label it 'Parallelogram', ensuring it also shows an area of 12 square feet.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Rectangle
A rectangle is one of the simplest shapes, commonly found in everyday life. It's a four-sided figure where opposite sides are equal and parallel, and each angle is a right angle (90 degrees). The formula for calculating the area of a rectangle is straightforward:
- We use the formula: \( A = l \times w \), where \( A \) represents the area, \( l \) is the length, and \( w \) is the width.
- If a rectangle has a length of 4 feet and a width of 3 feet, its area would be \( 4 \times 3 = 12 \) square feet.
- By altering the dimensions to 6 feet by 2 feet, the area calculation remains consistent: \( 6 \times 2 = 12 \) square feet as well.
Parallelogram
A parallelogram might look a bit like a leaning rectangle, but it holds its own unique properties. Opposite sides are equal and parallel, just like a rectangle, but the angles can vary. The formula for finding a parallelogram's area is similar yet different:
- The formula is \( A = b \times h \), with \( b \) as the base and \( h \) as the height.
- The base is the bottom measurement, and the height is the perpendicular distance from the base to the opposite side.
- For our parallelogram, by setting the base to 4 feet and the height to 3 feet, the area becomes \( 4 \times 3 = 12 \) square feet.
Dimensions
Dimensions are crucial in understanding shapes and their properties. They are the measurable extents of a shape, including length, width, height, and base, defining the size and boundaries of a geometric figure. When determining the dimensions of a rectangle or a parallelogram for area purposes, remember:
- The product of these dimensions helps calculate the area, showing how much space an object covers.
- For a rectangle, you can experiment with different pairs of length and width that multiply to the desired area.
- A similar approach applies to parallelograms with different base and height combinations that give the same area.
