Math Problem Statement
he Area of Different Shapes We can find the areas of odd shapes by dividing them into a number of standard shapes, such as triangles and rectangles. Then we find the areas of the standard shapes using formulas and add the areas. Let's start with the formula to find the area of a rectangle.
Many odd shapes can be divided into multiple rectangular shapes. A rectangle is a four-sided figure, or quadrilateral, with
all of its interior angles equal to 90 degrees, and opposite sides that are parallel and have the same length. A square is a rectangle where all four sides have the same length.
The area of a rectangle is calculated by multiplying its width and its length: area = length × width.
In rectangle ABCD, the width is represented by side AD and side BC, equal to 3 units, and the length is represented by sides AB and DC, equal to 6 units. Let's calculate the area of rectangle ABCD using the formula: area = (AD × AB) or (BC × DC) or (AD × DC) or (BC × AB).
Using the given values, we get the area of rectangle ABCD: area = 6 × 3 = 18 square units.
Solution
You're absolutely right! The area of a rectangle is indeed calculated by multiplying its length by its width, and this is a straightforward way to calculate the area of shapes like rectangles and squares.
To recap the steps you followed:
- You identified the rectangle ABCD with dimensions of width 3 units (AD = BC) and length 6 units (AB = DC).
- You applied the area formula: area = length × width.
- Then you substituted the given values: area = 6 × 3 = 18 square units.
Would you like to explore more shapes or have further questions on this topic?
Here are 5 related questions to help you explore further:
- How would you calculate the area of a triangle?
- What is the formula for the area of a circle?
- How can you calculate the area of irregular polygons?
- How does the formula for the area of a square differ from that of a rectangle?
- What is the difference between perimeter and area?
Tip: Always double-check that you are using the correct measurements (length and width) for the shape you are calculating, and ensure that the units are consistent (e.g., all in centimeters or inches).
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Math Problem Analysis
Mathematical Concepts
Geometry
Area of Shapes
Rectangles
Squares
Formulas
area = length × width
Theorems
Properties of Rectangles
Suitable Grade Level
Grades 5-7