CAIE IGCSE Mathematics Pythagoras Questions

Practise identifying the hypotenuse and applying Pythagoras' theorem to calculate missing lengths in right-angled plane and solid diagrams.

Exam points

identify the side opposite the right angle as the hypotenuse before forming the squared equation
add the two shorter-side squares for a hypotenuse or subtract one square for a shorter side
take the positive square root and use the calculated length in perimeter, area or a linked triangle

Covered syllabus points

C6.1.1 Know and use Pythagoras’ theorem.

[Maximum number: 5]

Figure for Question C6.1 Pythagoras’ theorem question 1 — CAIE IGCSE Mathematics Core

NOT TO SCALE

An isosceles triangle has base 12 cm and sides 16 cm. Find the area of this triangle.
$\mathrm{cm}^2$

The height is
$\sqrt{16^2-\left(\frac{12}{2}\right)^2}=\sqrt{220}.$
Hence the area is
$\frac12\times12\times\sqrt{220}=6\sqrt{220}=89.0\ \mathrm{cm^2}\ \text{(approximately)}.$

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Covered syllabus points

C6.1 Pythagoras’ theorem question 1