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Area, SM-Bank 135

A shape consisting of a quadrant and a right-angled triangle is shown.
 

  1. Use Pythagoras' Theorem to calculate the radius of the quadrant.  (2 marks)

  2. What is the area of this shape, correct to one decimal place?  (2 marks)
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a.    \(8\ \text{cm}\)

b.    \(74.3\ \text{cm}^2\ (1\text{d.p.})\)

Show Worked Solution

a.    \(\text{Using Pythagoras to find radius}\ (r):\)

\(a^2+b^2\) \(=c^2\)
\(r^2+6^2\) \(=10^2\)
\(r^2\) \(=10^2-6^2\)
\(r\) \(=\sqrt{64}\)
  \(=8\ \text{cm}\)

 

b.    \(\text{Total area}\) \(=\text{Area of triangle}+\text{Area of quadrant}\)
    \(=\dfrac{1}{2}\times 8\times 6+\dfrac{1}{4}\times \pi\times 8^2\)
    \(=24+50.265\dots\)
    \(=74.265\dots\)
    \(\approx 74.3\ \text{cm}^2\ (1\text{d.p.})\)