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Area, SM-Bank 101

The triangle below is isosceles.

  1. Use Pythagoras' Theorem to calculate the perpendicular height (\(h\)) of the triangle.  (2 marks)

  2. Using your answer from (a), find the area of the triangle.  (2 marks)

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a.    \(12\ \text{m}\)

b.    \(60\ \text{m}^2\)

Show Worked Solution

a.   

\(a^2+b^2\) \(=c^2\)
\(h^2+5^2\) \(=13^2\)
\(h^2\) \(=13^2-5^2\)
\(h^2\) \(=144\)
\(h\) \(=12\)

 
\(\therefore\ \text{The perpendicular height of the triangle is }12\ \text{m}\)
 

b.    \(\text{Area}\) \(=\dfrac{1}{2}\times bh\)
    \(=\dfrac{1}{2}\times 10\times 12\)
    \(=60\ \text{m}^2\)

Area, SM-Bank 100

Calculate the area of the following triangles.

  1.  
    (2 marks)

  2.   
    (2 marks)

  3.   
        (2 marks)

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a.    \(87.42\ \text{m}^2\)

b.    \(1995\ \text{mm}^2\)

c.    \(6650\ \text{m}^2\ \text{or}\ 0.665\ \text{m}^2\)

Show Worked Solution
a.    \(\text{Area}\) \(=\dfrac{1}{2}\times bh\)
    \(=\dfrac{1}{2}\times 12.4\times 14.1\)
    \(=87.42\ \text{m}^2\)

 

b.    \(\text{Area}\) \(=\dfrac{1}{2}\times bh\)
    \(=\dfrac{1}{2}\times 42\times 95\)
    \(=1995\ \text{mm}^2\)

 

c.    \(\text{Area in (cm)}^2\) \(=\dfrac{1}{2}\times bh\)
    \(=\dfrac{1}{2}\times 95\times 140\)
    \(=6650\ \text{cm}^2\)
 

 
\(\text{Area in (m)}^2\)		  
\(=\dfrac{1}{2}\times 0.95\times 1.40\)
    \(=0.665\ \text{m}^2\)

 

Area, SM-Bank 099

Calculate the area of the following triangles.

  1.  
    (2 marks)

  2.  
    (2 marks)

  3.  
      (2 marks)

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a.    \(42\ \text{cm}^2\)

b.    \(17.5\ \text{m}^2\)

c.    \(24\ \text{mm}^2\)

Show Worked Solution
a.    \(\text{Area}\) \(=\dfrac{1}{2}\times bh\)
    \(=\dfrac{1}{2}\times 12\times 7\)
    \(=42\ \text{cm}^2\)

 

b.    \(\text{Area}\) \(=\dfrac{1}{2}\times bh\)
    \(=\dfrac{1}{2}\times 5\times 7\)
    \(=17.5\ \text{m}^2\)

 

c.    \(\text{Area}\) \(=\dfrac{1}{2}\times bh\)
    \(=\dfrac{1}{2}\times 6\times 8\)
    \(=24\ \text{mm}^2\)

Area, SM-Bank 098

Label the base (\(b\)) and draw and label a line indicating the perpendicular height (\(h\)), on the following triangles.

a.   (1 mark)

                      b.    (1 mark)

                   

c.   (1 mark)
   
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a. 

                     b. 

                   

c. 

   
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a. 

                     b. 

                   

c. 

   
         
         

Area, SM-Bank 097

Identify the base (\(b\)) and the perpendicular height (\(h\)), by labelling the following triangles.

a.   (1 mark)

                      b.    (1 mark)

                   

c.   (1 mark)
   
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a. 

                     b. 

                   

c. 

   
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a. 

                     b. 

                   

c. 

   

Area, SM-Bank 043

Calculate the area of the following shapes in square units.

  1.  
              (1 mark)

     

  2.       
            (1 mark)

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a.    \(12\ \text{square units}\)

b.    \(10\ \text{square units}\)

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a.    \(\text{Area}=4\times 3=12\ \text{square units}\)

b.    \(\text{Area}\) \(=\text{Triangle }1+\text{Triangle }2\)
    \(=\dfrac{1}{2}\times 15+\dfrac{1}{2}\times 5\)
    \(=10\ \text{square units}\)

 

Area, SM-Bank 032 MC

A flag consists of three different coloured sections: red, white and blue.

The flag is 3 m long and 2 m wide, as shown in the diagram below.
 

The blue section is an isosceles triangle that extends to half the length of the flag.

The area of the blue section, in square metres, is

  1.  1.5
  2.  2
  3.  3
  4.  6
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\(A\)

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\(\text{Perpendicular height}\ \Delta=\dfrac{1}{2}\times 3=1.5\ \text{m}\)

\(\text{Area }\Delta\) \(=\dfrac{1}{2}\times bh\)
  \(=\dfrac{1}{2}\times 2\times 1.5\)
  \(= 1.5\ \text{m}^2\)

 
\(\Rightarrow A\)

Area, SM-Bank 011

This triangle was made by cutting a square in half.
 

 
The perimeter of the triangle is 51.21 cm.

What is the area of the triangle?  (2 marks)

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\(112.5\ \text{cm}^2\)

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\(\text{Triangle is isosceles with perimeter}=51.21\ \text{cm.}\)

\(\Rightarrow\ \text{Length of triangle side}\)

\(=\dfrac{1}{2}\times (51.21 – 21.21)\)

\(=\dfrac{1}{2}\times 30\)

\(=15\ \text{cm}\)

\(\therefore\ \text{Area}\) \(=\dfrac{1}{2}\times bh\)
  \(=\dfrac{1}{2}\times 15\times 15\)
  \(=112.5\ \text{cm}^2\)

Area, SM-Bank 009

Jill is playing in her parents' rectangular courtyard.

The courtyard is measured at 6 metres by 10 metres.

Jill draws a triangle on the courtyard with chalk, pictured below.

What is the area of this triangle?  (2 marks)
 

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\(14\ \text{m}^2\)

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\(\text{Base}=7\ \text{m}, \text{ Height}=4\ \text{m}\)

\(\text{Area of}\ \Delta\) \(=\dfrac{1}{2}\times bh\)
  \(=\dfrac{1}{2}\times 7\times 4\)
  \(=14\ \text{m}^2\)

Area, SM-Bank 007 MC

A triangle is drawn on grid paper.
 

 What is the area of the triangle?

  1. \(6\ \text{square units}\)
  2. \(8\ \text{square units}\)
  3. \(12\ \text{square units}\)
  4. \(16\ \text{square units}\)
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\(B\)

Show Worked Solution

\(\text{Area}\) \(=\dfrac{1}{2}\times bh\)
  \(=\dfrac{1}{2}\times 4\times 4\)
  \(= 8\ \text{square units}\)

 
\(\Rightarrow B\)

Area, SM-Bank 006 MC

A triangle is drawn on grid paper.
  

 What is the area of the triangle?

  1. \(15\ \text{square units}\)
  2. \(16\ \text{square units}\)
  3. \(18\ \text{square units}\)
  4. \(20\ \text{square units}\)
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\(A\)

Show Worked Solution

\(\text{Area}\) \(=\dfrac{1}{2}\times bh\)
  \(=\dfrac{1}{2}\times 6\times 5\)
  \(= 15\ \text{square units}\)

 
\(\Rightarrow A\)

Area, SM-Bank 001 MC

Which triangle has an area greater than 4 square units?
 

  1. \(\text{Triangle A}\)
  2. \(\text{Triangle B}\)
  3. \(\text{Triangle C}\)
  4. \(\text{Triangle D}\)
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\(B\)

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\(\text{Consider All options:}\)

\(\text{Triangle A}\) \(=\dfrac{1}{2}\times 3\times 2=3\ \text{square units}\)
\(\text{Triangle B}\) \(=\dfrac{1}{2}\times 3\times 3=4.5\ \text{square units}\ \checkmark\)
\(\text{Triangle C}\) \(=\dfrac{1}{2}\times 2\times 4=4\ \text{square units}\)
\(\text{Triangle D}\) \(=\dfrac{1}{2}\times 1\times 6=3\ \text{square units}\)

 
\(\Rightarrow B\)