Edexcel IGCSE Math B 6.F Pythagoras in 2D & 3D Question Bank

Practise applying Pythagoras in plane and solid diagrams, including coordinates, circles, compound lengths and 3D distances.

Exam points

calculate unknown sides in right-angled triangles from labelled diagrams
use repeated Pythagoras for 3D lengths, diagonals or compound routes
form equations or inequalities from Pythagoras in coordinate and circle problems

[Maximum number: 2]

Figure for Question 6.F Pythagoras in 2D and 3D question 1 — Edexcel IGCSE Math B

Figure 3 shows a solid right prism ABCDEFGH.
Diagram NOT accurately drawn.
The base of the prism, ABCD, is a rectangle and is horizontal. Trapezium BCHG is a cross section of the prism.
$AB=4\text{ m},\quad BC=3\text{ m},\quad CH=2.4\text{ m},\quad GB=1.5\text{ m}$ $\angle GBC=\angle BCH=\angle ABG=\angle DCH=90^\circ$

Calculate the length, in metres to 3 significant figures, of AH.

$AH=\sqrt{4^{2}+3^{2}+2.4^{2}} = \sqrt{30.76}$
Final answer:
$5.55\text{ m}$

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6.F Pythagoras in 2D and 3D question 1