How to find the area of an L-shape?
Understand the Problem
The question is asking for the method to calculate the area of a figure that has an L shape. This involves understanding how to break down the L-shape into simpler geometric figures whose areas can be calculated.
Answer
The area of the L-shape is given by $A = w_1 \times h_1 - w_2 \times h_2$.
Answer for screen readers
Let the dimensions of the larger rectangle be $w_1$ and $h_1$, and the dimensions of the smaller rectangle be $w_2$ and $h_2$. The area of the L-shape is given by:
$$ A = w_1 \times h_1 - w_2 \times h_2 $$
Steps to Solve
- Break down the L-shape into rectangles
Identify the dimensions of the two rectangles that make up the L-shape. Assign labels for each rectangle, such as width and height. For example, if the larger rectangle has a width of $w_1$ and a height of $h_1$, and the smaller rectangle has a width of $w_2$ and a height of $h_2$, make sure you keep track of these measurements.
- Calculate the area of each rectangle
Use the area formula for rectangles, which is Area = Width × Height.
For the larger rectangle: $$ A_1 = w_1 \times h_1 $$
For the smaller rectangle: $$ A_2 = w_2 \times h_2 $$
- Subtract the area of the smaller rectangle from the larger rectangle
The area of the L-shape can then be found by subtracting the area of the smaller rectangle from the area of the larger rectangle.
$$ A = A_1 - A_2 $$
This gives the total area for the L-shaped figure.
Let the dimensions of the larger rectangle be $w_1$ and $h_1$, and the dimensions of the smaller rectangle be $w_2$ and $h_2$. The area of the L-shape is given by:
$$ A = w_1 \times h_1 - w_2 \times h_2 $$
More Information
This method for finding the area of an L-shape applies to any configuration of the shape as long as it can be split into two rectangles. The area can also help in practical applications, such as determining flooring space, painting walls, or landscaping.
Tips
- Forgetting to subtract the correct area of the smaller rectangle from the larger rectangle. Always ensure you correctly identify which rectangle is larger.
- Mislabeling the dimensions of the rectangles leading to calculation errors. Take care to label and record dimensions accurately.
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