Areas of Rectilinear Figures — Lesson
1) Hook — A Fun Real-Life Story to Grab Your Attention
Imagine you are helping your uncle design a beautiful garden in his backyard in Jaipur. The garden has a unique shape made by joining several rectangular and square flower beds. To buy the right amount of soil and grass, you need to find the total area of this irregular-shaped garden. How would you calculate it easily? This is where the concept of Areas of Rectilinear Figures becomes very useful!
2) Core Concepts — Understanding Areas of Rectilinear Figures
A rectilinear figure is a polygon whose sides meet at right angles (90°). It looks like a shape made by joining rectangles and squares together. To find its area, we divide the figure into smaller rectangles or squares, find the area of each, and then add them up.
Step-by-step method:
- Divide the rectilinear figure into rectangles/squares by drawing imaginary lines.
- Calculate the area of each rectangle/square using Area = length × breadth.
- Add all the areas to get the total area of the figure.
Example:
| Part | Length (m) | Breadth (m) | Area (m²) |
|---|---|---|---|
| Rectangle A | 8 | 5 | 40 |
| Rectangle B | 3 | 5 | 15 |
Total area = Area of A + Area of B = 40 + 15 = 55 m²
3) Key Formulas / Rules
Area of Rectangle = Length × Breadth
Area of Square = Side × Side
Area of Rectilinear Figure = Sum of areas of all rectangles/squares it is divided into
4) Did You Know?
The famous Indian mathematician Bhāskara II (12th century) worked extensively on geometry and areas. His book “Lilavati” contains many interesting problems on areas and shapes, showing how ancient Indian scholars contributed to mathematics long before modern formulas were formalized!
5) Exam Tips — Avoid These Common Mistakes!
- Always label dimensions clearly when dividing the figure; do not assume missing lengths without calculation.
- Check units carefully — convert all measurements to the same unit before calculating area.
- Do not forget to add all parts’ areas at the end; partial answers lose marks.
- Practice drawing the figure and dividing it neatly; examiners appreciate clear diagrams.
- Board exam questions often ask for area of a given rectilinear figure or missing dimension using area. Practice both types.
Areas of Rectilinear Figures — Mcq
Areas of Rectilinear Figures — Mnemonic
Mnemonic 1: AREA FUN for Rectilinear Figures 📐✨
- Always Remember Each Area by breaking into rectangles!
- “Divide and Conquer” – Split complex shapes into rectangles, find each area, then add up!
- Hindi Hint: "Chhote-chhote hisse, jodo sabse pehle!" (Break into small parts, then add all!)
Mnemonic 2: RECTANGLE Trick 🎯
- Rectangles first, Easy to find area,
- Cut the figure into parts,
- Total area is sum of all,
- Add length × breadth smartly,
- Never forget to add,
- Geometry made simple,
- Learn, split, and solve,
- Easy peasy, done!
Mnemonic 3: Funny Hindi Rhyme for Areas 🎉
"Area ka formula yaad rakhna bhai,
Rectangle banake karna kaam aasan hai,
Length times breadth se niklega jawab,
Har hisse ka alag area jodna ka kaam." 😊
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