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Recatangles and Triangles

This document provides exercises to estimate the area of triangles by comparing them to rectangles. It asks students to calculate the areas of various rectangles and triangles formed by combining geometric shapes. It also introduces a pattern of overlapping triangles and asks students to describe the relationship between the number of an triangle in the pattern and its area. Finally, it prompts students to draw more triangles on grid paper and look for generalizations about the relationship between a triangle's dimensions and its area.

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unknownname19901
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241 views10 pages

Recatangles and Triangles

This document provides exercises to estimate the area of triangles by comparing them to rectangles. It asks students to calculate the areas of various rectangles and triangles formed by combining geometric shapes. It also introduces a pattern of overlapping triangles and asks students to describe the relationship between the number of an triangle in the pattern and its area. Finally, it prompts students to draw more triangles on grid paper and look for generalizations about the relationship between a triangle's dimensions and its area.

Uploaded by

unknownname19901
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PPTX, PDF, TXT or read online on Scribd
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Exploring measures

Rectangles and Triangles


We are going to….
● estimate the area of a triangle
● work out the area of triangles using
rectangles
Exercise 7.1
1. This rectangle was made by putting two squares together.

6 cm
a. What is the area of the rectangle?
b. What is the area of one of the squares?
2. This square was made by putting two identical rectangles together.

9 cm
a. What is the area of the square?
b. What is the are of one of the rectangles?
3. Asok took two pieces of paper.

He cut one piece of paper in half, like picture A.


a. What was the area of the piece of paper before it was cut?
b. What is the area of one of the smaller pieces of paper Asok
made?
He cut the other piece of paper in half, like picture B.
c. What is the are of one of the smaller pieces of paper Asok
made?
4. Estimate the area of these triangles by counting the squares.

What knowledge are you using about squares to help you


decide if a square if half covered by a shape? What different
ways do you think a square can be cut into two equal pieces
with a straight line? Talk to a partner about your ideas.
5. Selena made this pattern by overlapping tissue paper triangles.

Here are the bottom three triangles, as they look an


a centimetre square grid.

a. Draw and complete a table to show the area of each triangle in the pattern.
b. What would be the are of the 7th triangle?
c. What would be the are of the 10th triangle?
d. Look at the pattern of numbers in your table. Try to describe the pattern of the areas of the triangle.
Can you think of a way to always predict what the area of the next triangle will be?
Generalise by describing the link between the number of each triangle and its area.
Think like a mathematician
What is the area of each of these picture?
Each triangle is drawn on centimetre squared paper.
Count the squares to estimate the area of each triangle.

Characterise by describing what you


notice about the area of the triangles
from your estimates.
Draw more triangles on squared paper
inside rectangles that are 8 cm by 4
cm.
Each triangle should be as wide and
as tall as the rectangle.
Estimate the area of the triangles you
draw by counting squares.
Generalise by describing what you find
out.
Work example 1
6. These rectangles are cut in half diagonally to make two triangles.
For each diagram work out the area of the rectangle and the area of one of the triangles.
7. Work out the are of the rectangle.

8. Jo makes triangular biscuits by cutting out 5 cm squares of dough, then cutting them in half.

Jo wants to cover each biscuit in icing.


This tub of icing covers 340 cm² of biscuit.
How many triangular biscuits will Jo be able to cover?

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