Area of Combined Shapes

By Jason Granada

Area of Composite Figures

​Let's have a short review. You have 20 seconds to answer the questions.

Multiple Choice

_________ is a scalar quantity that refers to “how fast an object is moving.

• Speed

• Distance

• Time

• Equation

Multiple Choice

________ is a total length of space between two positions.

• Speed

• Distance

• Time

• Average Speed

Multiple Choice

________ is the quantity measured or measurable period during which an action, process, or condition exists or continuous.

• Speed

• Distance

• Time

• Average Speed

Multiple Choice

A football field is about 90meters long. If it took Eduardo 20 seconds to run its length, how fast was he running?

• 4 m/sec.

• 4.5 m/sec

• 5 m/sec.

• 5.5 m/sec.

Multiple Choice

If you drive at 120 km/hr for 5 hours, how far will you go?

• 300 km

• 400 km

• 500 km

• 600 km

Area of Composite Figures

The module is divided into two lessons, namely:

• Lesson 1 – Finding the area of composite figures formed by any two ormore of the following: square, rectangle, circle and semi-circle

• Lesson 2 – Solving routine and non-routine problems involving area ofcomposite figures formed by any two or more of the followingtriangle, square, rectangle, circle and semi-circle

Before we start studying this module, take this simple test first to find out how much you already know about the topics to be discussed.

Encircle the letter of the composite figures on your screen.

Multiple Choice

Find the area of this figure.

• 64 cm²

• 16 cm²

Multiple Choice

Find the area of this figure.

• 72 cm²

• 36 cm²

Draw

Find the area of this figure.

Exploring Composite of Figures

Aaron was plotting the shape of his garden on grid paper. While it was anirregular shape, it was perfect for his yard. Each square on the gridrepresents 1 square meter.

A. Describe one way you can find the area fo this garden.

B. ​The area of this garden is _________ square meters.​

Finding the Area of a Composite Figure

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A composite figure is made up of simple geometric shapes. To find the area of a composite figure or other irregular-shaped figure, divide it into simple, nonoverlapping figures. Find the area of each simpler figure, and then add the areas together to find the total area of the composite figure.

​

Use the chart to review

some common area

formulas.

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Exploring Composite of Figures

Aaron was plotting the shape of his garden on grid paper. While it was anirregular shape, it was perfect for his yard. Each square on the grid represents 1 square meter.

Using Area to Solve Problem

A banquet room is being carpeted. A floor plan of the room is shown at right. Each unit represents1 yard. The carpet costs Php 1000 per square yard. How much will it cost to carpet the room?

​Step 1: Separate the composite figure into simpler shapes as shown by the dashed lines: a parallelogram, a rectangle, and a triangle.

Using Area to Solve Problem

A banquet room is being carpeted. A floor plan of the room is shown at right. Each unit represents1 yard. The carpet costs Php 1000 per square yard. How much will it cost to carpet the room?

​Step 2 Find the area of the simpler figures. Count units to find the dimensions.

Using Area to Solve Problem

A banquet room is being carpeted. A floor plan of the room is shown at right. Each unit represents1 yard. The carpet costs P1000.00 per square yard. How much will it cost to carpet the room?

​Step 3 Find the area of the composite figure.

A = 8 + 24 + 1 = 33 square yards​

​Step 4 Calculate the cost to carpet the room.

Area x Cost per yard = Total cost

33 x P1000.00 = P 33,000.00

​

The cost to carpet the banquet room is P 33,000.00