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Middle Years

10.04 Area of triangles

Worksheet
Triangles and rectangles
1

Consider the rectangle shown:

a

Find the area of the entire rectangle.

b

Find the area of the triangle.

c

What do you notice about the two areas?

2

For each of the following figures:

i

Find the area of the entire rectangle.

ii

Find the area of the shaded triangle.

a
b
c
d
e
f
3

Consider the following triangle:

Which dimension of the following rectangle forms the height of the inside triangle?

Area of a triangle
4

Find the area of the following triangles:

a
b
c
d
e
5

Find the area of a triangle which has the following dimensions:

a
Height =8\text{ cm} and base =9\text{ cm}.
b
Height =4\text{ m} and base =6\text{ m}.
c
Height =7\text{ mm} and base =8\text{ mm}.
d
Height =3\text{ cm} and base =9\text{ cm}.
Dimensions from area
6

For each of the following triangles, find the value of b or h given the area:

a

Area =20\text{ mm}^2

b

Area =48\text{ m}^2

7

Determine whether the following could be the dimensions of a triangle with an area of 20\text{ mm}^2:

a

Base =8\text{ mm}, height =5\text{ mm}.

b

Base =1\text{ mm}, height =20\text{ mm}.

c

Base =5\text{ mm}, height =8\text{ mm}.

d

Base =2\text{ mm}, height =20\text{ mm}.

8

Complete the following table of base and height measurements for different triangles, which all have an area of 30\text{ m}^2:

\text{Base (m)}1015
\text{Height (m)}12
\text{Area (m}^2)303030
Applications
9

Lisa has purchased a rectangular piece of fabric measuring 6\text{ m} in length and 9\text{ m} in width. Find the area of the largest triangular piece she can cut out from it.

10

A gutter running along the roof of a house has a cross-section in the shape of a triangle as shown:

If the area of the cross-section is 40\text{ cm}^2, and the length of the base of the gutter is 10\text{ cm}, find the perpendicular height h of the gutter.

11

The faces on a 4-sided die are all triangular. Each face has a base length of 19\text{ mm} and a perpendicular height of 12\text{ mm}. Find the area of one face.

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