What is Area of a Composite Figure?

S3-SA2-0117

Grade Level:

Class 7

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

A composite figure is a shape made by combining two or more simple shapes like rectangles, triangles, or circles. The area of a composite figure is the total space it covers, found by adding or subtracting the areas of these simpler shapes.

Simple Example

Quick Example

Imagine your school playground has a rectangular cricket pitch attached to a semicircular seating area. To find the total area of the playground, you would find the area of the rectangle and the area of the semicircle separately, then add them up. That's finding the area of a composite figure!

Worked Example

Step-by-Step

Let's find the area of a figure made of a rectangle (length = 10 cm, width = 5 cm) and a triangle on top (base = 10 cm, height = 4 cm).

Step 1: Identify the simple shapes. Here, it's a rectangle and a triangle.

---

Step 2: Calculate the area of the rectangle. Area of rectangle = length x width = 10 cm x 5 cm = 50 sq cm.

---

Step 3: Calculate the area of the triangle. Area of triangle = 0.5 x base x height = 0.5 x 10 cm x 4 cm = 20 sq cm.

---

Step 4: Add the areas of the simple shapes to get the total area. Total Area = Area of rectangle + Area of triangle = 50 sq cm + 20 sq cm = 70 sq cm.

---

The total area of the composite figure is 70 sq cm.

Why It Matters

Understanding composite figures helps engineers design buildings and bridges efficiently, ensuring they use the right amount of materials. In Computer Science, graphic designers use this to calculate space for elements on a screen. Even city planners use it to estimate land use for parks and roads!

Common Mistakes

MISTAKE: Forgetting to break down the complex shape into simpler, known shapes. | CORRECTION: Always start by visually dividing the composite figure into basic shapes like squares, rectangles, triangles, or circles.

MISTAKE: Using the wrong formula for a simple shape (e.g., using perimeter formula instead of area). | CORRECTION: Double-check that you are using the correct area formula for each individual simple shape before calculating.

MISTAKE: Adding areas when a part of the figure is cut out (subtracted). | CORRECTION: If a part is removed from a larger shape, you must subtract its area from the larger shape's area, not add it.

Practice Questions

Try It Yourself

QUESTION: A figure is made of a square with side 6 cm and a semicircle attached to one of its sides. Find the total area (use pi = 3.14). | ANSWER: Area of square = 6x6 = 36 sq cm. Radius of semicircle = 6/2 = 3 cm. Area of semicircle = 0.5 x 3.14 x 3^2 = 0.5 x 3.14 x 9 = 14.13 sq cm. Total Area = 36 + 14.13 = 50.13 sq cm.

QUESTION: A rectangular park (length 20m, width 15m) has a triangular flower bed cut out from one corner (base 5m, height 4m). What is the area of the remaining park? | ANSWER: Area of rectangle = 20x15 = 300 sq m. Area of triangle = 0.5 x 5 x 4 = 10 sq m. Remaining area = 300 - 10 = 290 sq m.

QUESTION: A floor plan looks like an 'L' shape. It can be divided into two rectangles: Rectangle A (length 8m, width 3m) and Rectangle B (length 5m, width 2m). Find the total area of the floor. | ANSWER: Area of Rectangle A = 8x3 = 24 sq m. Area of Rectangle B = 5x2 = 10 sq m. Total Area = 24 + 10 = 34 sq m.

MCQ

Quick Quiz

Which of these is NOT a step in finding the area of a composite figure?

Breaking the figure into simpler shapes

Calculating the perimeter of each simple shape

Calculating the area of each simple shape

Adding or subtracting the areas of the simple shapes

The Correct Answer Is:

To find the area of a composite figure, you need to calculate the *area* of each simple shape, not its perimeter. Perimeter is about the boundary length, not the space covered.

Real World Connection

In the Real World

When architects design houses in India, they often work with 'L' shaped rooms or rooms with alcoves. To calculate the amount of tiles needed for the floor, they break down these complex room shapes into simpler rectangles and squares to find the total area. This ensures they buy the correct quantity of tiles, avoiding wastage or shortages.

Key Vocabulary

Key Terms

COMPOSITE FIGURE: A shape made by combining two or more simple shapes | AREA: The amount of space a 2D shape covers | RECTANGLE: A four-sided shape with all angles 90 degrees | TRIANGLE: A three-sided polygon | SEMICIRCLE: Half of a circle

What's Next

What to Learn Next

Great job understanding composite figures! Next, you can explore finding the volume of composite solids. Just like 2D shapes combine, 3D shapes can also be combined, and you'll use similar ideas to calculate their total space!