Area by Adding Parts
Grade 8 math lesson on finding the area of irregular shapes by breaking them into smaller parts and adding the areas. Students practice decomposing complex figures into rectangles and triangles, calculating each part separately, and summing the results.
Key Concepts
Property The area of some polygons can be found by dividing the polygon into smaller parts and finding the area of each part.
Examples A trapezoid is split into a rectangle and a triangle. Area = $(7 \cdot 5) + \frac{1}{2}(2 \cdot 5) = 35 + 5 = 40 \text{ cm}^2$. An L shaped figure is split into two rectangles. Area = $(8 \text{ ft} \cdot 6 \text{ ft}) + (4 \text{ ft} \cdot 4 \text{ ft}) = 48 + 16 = 64 \text{ ft}^2$.
Explanation Think of a weirdly shaped polygon as a puzzle! You can't solve it all at once. So, you break it into easy shapes you already know, like rectangles and triangles. Find the area of each piece, add them all up, and voilà! You have solved the big puzzle and found the total area.
Common Questions
How do you find the area of an irregular shape by adding parts?
Divide the irregular shape into simpler shapes like rectangles and triangles. Calculate the area of each simpler shape using its formula, then add all the areas together to get the total area.
How do you decide how to split an irregular figure?
Look for natural dividing lines like right angles, horizontal or vertical lines that extend through the shape. Draw lines that create simpler shapes (rectangles, right triangles) and label the dimensions of each part.
What formulas do you need to know for finding area by adding parts?
You need: rectangle area = length times width, triangle area = 1/2 base times height, and sometimes trapezoid area = (b1+b2)/2 times height. Most composite figures can be broken into rectangles and triangles.
What is a common mistake when finding area by adding parts?
A common mistake is using incorrect dimensions for each part. Carefully label each dimension from the original figure, calculate any missing lengths by subtraction, and double-check that your parts together cover exactly the original shape.