Area and perimeter of my name

How would you create each letter of your name on graph paper?

Record your ideas in a notebook or a method of your choice.

How could you determine the total area and perimeter of all the letters combined? What strategies could you use?

Here is an example!

If you would like, you can complete the activity using TVO Mathify. You can also use your notebook or the following fillable and printable document.

To help you find the area and perimeter of your name, you may want a few tips. Press ‘Hint’ to reveal these tips.

Hint

Task 1: Calculating perimeter

What is perimeter?

Perimeter is the measurement of the outside lengths of a shape.

Consider some ways you can answer this example question: What is the rectangle’s perimeter?

Record your ideas in a notebook or a method of your choice.

When you are ready, press ‘Show Answer’ to reveal the solution.

Show Answer

Complete the activities with the following shapes. Record your answers in a notebook or a method of your choice. We will compare our answers after.

1. What is the perimeter of the rectangle? How did you know what all the side lengths were of this shape, even though not all were labelled?

Press ‘Hints’ to reveal perimeter hints for a rectangle.

Hints

2. What is the perimeter of this shape? How can you know even though not all side lengths are given? Press ‘Hint’ to reveal a perimeter hint for this arrow shape.

Hint

3. The total perimeter of the following rectangle is 48 cm. What are the lengths of the missing sides?

When you are ready, press ‘Show Answer’ to reveal the solutions.

Show Answer

Task 2: Calculating area

When calculating area:

• Area is defined as the size of a surface. It is the space inside of a two-dimensional shape.
• The units are squared because area is calculated as a product of two dimensions.
• There are different formulas for calculating the area of different shapes.

Area of parallelograms, squares, and rectangles

The formula to calculate the area of parallelograms, squares, or rectangles is:

Area = b × h

b = base

h = height

For the following questions, record your answers in a notebook or a method of your choice.

1. How would you calculate the area of a rectangle with an 8 cm base and 4 cm height?

When you are ready, press ‘Show Answer’ to reveal the solutions.

Show Answer

2. Area of parallelogram is base × height. Calculate the area of the following parallelogram with 16 cm base and 10 cm height.

Area of a triangle

The formula for calculating the area of a triangle is:

Area $=b\times h÷2$

This formula can be displayed in different ways:

• Area $=b\times h÷2$
• Area $=\frac{1}{2}\left(b\times h\right)$
• Area $\frac{b\times h}{2}$

In what ways are these formulas the same? What is different about them? Which one do you prefer to use?

For the following questions, please record your calculations in a notebook or a method of your choice.

How would you calculate the area of the following triangle with base of 20 cm and height of 15 cm?

When you are ready, press ‘Show Answer’ to reveal the solutions.

Show Answer

Calculate the area of the following right triangle with 6 centimetres as base and height. Press ‘Hint’ to reveal a perimeter hint for this shape.

Hint

Two methods for finding the area of a trapezoid

The following shape is an example of a trapezoid.

What other shapes are within the trapezoid?

Using the information you already have about calculating the area of other shapes, how can you figure out the area of a typical trapezoid? There are many different ways to calculate the area of a trapezoid.

The trapezoid can be decomposed into rectangles, parallelograms, or triangles in different ways.

Here are 2 ways to calculate the area of a trapezoid.

Trapezoid area method 1

Break up the original trapezoid into 2 triangles and 1 rectangle.

A trapezoid can be divided into 2 triangles and 1 rectangle.

• The formula is: area of triangle 1 (left side) + area of rectangle + area of triangle 2 (right side).

Here is an example of how this method could be used.

Area = area of triangle 1 + area of rectangle + area of triangle 2.

= (3 × 5 ÷ 2) + (6 × 5) + (3 × 5 ÷ 2)

= 7.5 + 30 + 7.5

= 45 cm²

Trapezoid area method 2

Double the original trapezoid so it becomes a parallelogram. Find the area of the parallelogram and then divide it by 2.

The diagram has two identical trapezoids, with one inverted, which have been put together to create a parallelogram.

The formula is $\left(b1+b2\right)\times h÷2.$

In other words: (Base 1 of first trapezoid $\left(b1\right)$   plus Base 2 of second Trapezoid $\left(b2\right)$   ) × height of trapezoid $h$ and divide by 2.

Here is an example of what this would be.

Area $=\left(b1+b2\right)\times h÷2$

$=\left(15+3\right)\times 15÷2$

$=18\times 15÷2$

$=135 c{m}^2$

Find the trapezoid area

If you would like, you can complete the next activity using TVO Mathify. You can also use your notebook or the following fillable and printable document. Choose one of the methods outlined earlier in this learning activity. Calculate the area of a trapezoid with the following dimensions. The base is 16 cm, height is 12 cm, and the top is 10 cm.

Press ‘Hint’ to reveal a perimeter hint for this shape.

Hint

Press the ‘TVO Mathify’ button to access this resource and the ‘Activity’ button for your note-taking document.

When you are ready, press ‘Show Answer’ to reveal the solutions.

Show Answer

A method for finding the area of a rhombus or a kite

The following diagram is a rhombus and a kite. In a rhombus, the diagonal (interior, blue) lines are equal, but in a kite, the diagonal lines are not equal.

What other shapes are within a rhombus or kite? Inside, you may notice four triangles: a pair of similar triangles on top, and a pair on the bottom. You could find the areas of the interior four triangle to get the area. However, there is a faster way. What if you used the diagonal (interior, blue) lines to form a rectangle around the kite or rhombus, as shown in the following diagram. You will now notice 4 interior and 4 exterior triangles.

The area of the four triangles outside the kite is equal to the area inside the kite. Therefore, the area of the kite (the four triangles) is half the area of the entire square (the eight triangles).

In other words, the formula for the area of a kite is: (length × width) divided by two.

How would you use this information to calculate the area $\left(A\right)$  of a kite that is measured 20 centimetres in one diagonal $\left(p\right)$ , and 30 centimetres in the other diagonal $\left(q\right)$ ? Here is one way to find the area of this kite.

Area = $p\times \mathrm{q}÷2$

Area = $20\times 30÷2$

Area = $600÷2$

Area = $300c{m}^2$

The area of this kite is $300c{m}^2.$

Task 3: Area and perimeter in real-life

Why is it relevant to understand how to calculate the area and perimeter of something?

Here are some instances when someone would need to calculate the area and perimeter of something:

• building a fence around a garden
• building a swimming pool
• creating a floor plan

Can you think of other instances?

Record your ideas in a notebook or a method of your choice.

Task 4: Calculating perimeter and area for irregular shapes

An irregular shape is any shape that has sides and angles that can be any size or length.

They do not have to be equal.

Challenge: Create any irregular shape. Use digital or concrete manipulatives.

Describe the shape. Record your ideas in a notebook or a method of your choice.

Perimeter of irregular shapes

In order to calculate the perimeter of irregular shapes, we follow the same instructions as a regular shape. Add up all side lengths to find the perimeter.

Consider

How might you calculate the perimeter of this irregular shape?

Press ‘Hint’ to reveal a perimeter hint for this shape.

Hint

Area of irregular shapes

In order to calculate the area of irregular shapes, we begin by dividing it into smaller, known shapes. Consider the following irregular shape.

Let’s calculate the area of the irregular shape.

Step 1: Divide your irregular shape into smaller, known shapes.

For this shape we can divide it into 1 square and 1 rectangle.

Step 2: Find the area of each smaller shape.

For this shape, we will find the area of the square and the rectangle.

Square:

Area = 2 × 2

= $4 c{m}^2$

Rectangle:

Area = 6 × 10

= $60 c{m}^2$

Step 3: Add all of the areas together.

$4 c{m}^2+60 c{m}^2=64 c{m}^2$

Area $=64 c{m}^2$

Task 5: Your turn!

Examine and solve each of the problems. Show your work and record your calculations in a notebook or a method of your choice. When you are ready, press ‘Show Answer’ to reveal a solution.

1. Find the area of the shape. Press ‘Hint’ to reveal a perimeter hint for this shape.

Hint

Show Answer

2. Find the area and perimeter of the shape.

Show Answer

3. Find the area of the shape given.

Show Answer

Task 1: Home design

A contractor has been tasked with creating a house. Let’s create a floor plan of what the house could be like.

The contractor also has a set of criteria to follow. The house must have rooms that are each of these shapes:

• rectangle
• square
• triangle
• trapezoid
• at least one irregular shaped room
• whatever other shapes you would like!

You will need to:

• create a floor plan for this home (each room, hallways, etc.)
• calculate the area and perimeter of each room
• calculate the area and perimeter of the home as a whole
• show your work to explain how you calculated each area and perimeter

Record your ideas in a notebook or a method of your choice.

Task 2: Questions to explore

Reflection

As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.

Now, record your ideas using a voice recorder, speech-to-text, or writing tool.

Connect with a TVO Mathify tutor