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Area, SM-Bank 149

A rhombus has an area of 250 square centimetres. If one diagonal measures 10 centimetres, find the length of the other diagonal.  (2 marks)

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\(50\ \text{cm}\)

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\(\text{Area of rhombus}=250\ \text{cm}^2\)

\(\text{Length of diagonal:}\ x=10\ \text{m}\)

\(A\) \(=\dfrac{1}{2}xy\)
\(250\) \(=\dfrac{1}{2}\times 10\times y\)
\(5y\) \(=250\)
\(y\) \(=\dfrac{250}{5}\)
  \(=50\ \text{cm}\)

 
\(\therefore\ \text{The other diagonal is }50\ \text{cm long.}\)

Area, SM-Bank 148

A rhombus has an area of 140.8 square metres. If one diagonal measures 16 metres, find the length of the other diagonal.  (2 marks)

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\(17.6\ \text{m}\)

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\(\text{Area of rhombus}=140.8\ \text{m}^2\)

\(\text{Length of diagonal:}\ x=16\ \text{m}\)

\(A\) \(=\dfrac{1}{2}xy\)
\(140.8\) \(=\dfrac{1}{2}\times 16\times y\)
\(8y\) \(=140.8\)
\(y\) \(=\dfrac{140.8}{8}\)
  \(=17.6\ \text{m}\)

 
\(\therefore\ \text{The other diagonal is }17.6\ \text{m long.}\)

Area, SM-Bank 147

Calculate the area of the following rhombus in millimetres squared.  (2 marks)

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\(96\ \text{mm}^2\)

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\(\text{Length of diagonal 1:}\ x=16\ \text{mm}\)

\(\text{Length of diagonal 2:}\ y=12\ \text{mm}\)

\(\text{Area of rhombus}\) \(=\dfrac{1}{2}xy\)
  \(=\dfrac{1}{2}\times 16\times 12\)
  \(=96\ \text{mm}^2\)

Area, SM-Bank 146

Calculate the area of the following rhombus. All measurements are in metres.   (2 marks)

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\(90.24\ \text{m}^2\)

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\(\text{Length of diagonal 1:}\ x=14.1\ \text{m}\)

\(\text{Length of diagonal 2:}\ y=12.8\ \text{m}\)

\(\text{Area of rhombus}\) \(=\dfrac{1}{2}xy\)
  \(=\dfrac{1}{2}\times 14.1\times 12.8\)
  \(=90.24\ \text{m}^2\)

Area, SM-Bank 145

Calculate the area of the following rhombus. All measurements are in metres.   (2 marks)

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\(76.44\ \text{m}^2\)

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\(\text{Length of diagonal 1:}\ x=2\times 4.2=8.4\ \text{m}\)

\(\text{Length of diagonal 2:}\ y=2\times 9.1=18.2\ \text{m}\)

\(\text{Area of rhombus}\) \(=\dfrac{1}{2}xy\)
  \(=\dfrac{1}{2}\times 8.4\times 18.2\)
  \(=76.44\ \text{m}^2\)

Area, SM-Bank 144

Calculate the area of the following rhombus. All measurements are in centimetres.   (2 marks)

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\(484\ \text{cm}^2\)

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\(\text{Length of diagonal 1:}\ x=2\times 11=22\ \text{cm}\)

\(\text{Length of diagonal 2:}\ y=2\times 22=44\ \text{cm}\)

\(\text{Area of rhombus}\) \(=\dfrac{1}{2}xy\)
  \(=\dfrac{1}{2}\times 22\times 44\)
  \(=484\ \text{cm}^2\)

Area, SM-Bank 143

Calculate the area of the following rhombus. All measurements are in millimetres.   (2 marks)

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\(24\ \text{mm}^2\)

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\(\text{Length of diagonal 1:}\ x=2\times 3=6\ \text{mm}\)

\(\text{Length of diagonal 2:}\ y=2\times 4=8\ \text{mm}\)

\(\text{Area of rhombus}\) \(=\dfrac{1}{2}xy\)
  \(=\dfrac{1}{2}\times 6\times 8\)
  \(=24\ \text{mm}^2\)

Area, SM-Bank 142

Calculate the area of the following kite. All measurements are in millimetres.   (2 marks)

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\(180\ \text{mm}^2\)

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\(\text{Length of diagonal 1:}\ x=4+11=15\ \text{mm}\)

\(\text{Length of diagonal 2:}\ y=2\times 12=24\ \text{mm}\)

\(\text{Area of kite}\) \(=\dfrac{1}{2}xy\)
  \(=\dfrac{1}{2}\times 34\times 20\)
  \(=180\ \text{mm}^2\)

Area, SM-Bank 141

Calculate the area of the following kite. All measurements are in metres.   (2 marks)

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\(340\ \text{m}^2\)

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\(\text{Length of diagonal 1:}\ x=26+8=34\ \text{m}\)

\(\text{Length of diagonal 2:}\ y=2\times 10=20\ \text{m}\)

\(\text{Area of kite}\) \(=\dfrac{1}{2}xy\)
  \(=\dfrac{1}{2}\times 34\times 20\)
  \(=340\ \text{m}^2\)

Area, SM-Bank 140

Calculate the area of the following kite. All measurements are in centimetres.   (2 marks)

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\(156\ \text{cm}^2\)

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\(\text{Length of diagonal 1:}\ x=8+18=26\ \text{cm}\)

\(\text{Length of diagonal 2:}\ y=2\times 6=12\ \text{cm}\)

\(\text{Area of kite}\) \(=\dfrac{1}{2}xy\)
  \(=\dfrac{1}{2}\times 26\times 12\)
  \(=156\ \text{cm}^2\)

Area, SM-Bank 134

A kite has an area of \(32\ 240\) square centimetres. Given that one of the diagonals has a length of 124 centimetres, calculate the length of the other diagonal.  (2 marks)

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\(520\ \text{cm}\)

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\(\text{Let the unknown diagonal}=x\)

\(A\) \(=\dfrac{1}{2}xy\)
\(32\ 240\) \(=\dfrac{1}{2}\times 124\times x\)
\(62x\) \(=32\ 240\)
\(x\) \(=\dfrac{32\ 240}{62}\)
  \(=520\ \text{cm}\)

Area, SM-Bank 133

A kite has an area of 52 square metres. Given that one of the diagonals has a length of 8 metres, calculate the length of the other diagonal.  (2 marks)

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\(13\ \text{m}\)

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\(\text{Let the unknown diagonal}=x\)

\(A\) \(=\dfrac{1}{2}xy\)
\(52\) \(=\dfrac{1}{2}\times 8\times x\)
\(4x\) \(=52\)
\(x\) \(=\dfrac{52}{4}\)
  \(=13\ \text{m}\)

Area, SM-Bank 132

Johan builds a kite with diagonals of 0.7 metres and 1.2 metres as shown below.

Calculate the area of Johan's kite (not including the tail) in square metres.   (2 marks)
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\(0.42\ \text{m}^2\)

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\(A\) \(=\dfrac{1}{2}xy\)
  \(=\dfrac{1}{2}\times 0.7\times 1.2\)
  \(=0.42\ \text{m}^2\)