IGCSE Math B 6.F Pythagoras in 2D and 3D Topic Practice

Diagram NOT accurately drawn

The diagram shows triangle ABC with $AB=50\text{ cm}$, $AC=25\text{ cm}$ and $\angle ACB=90^\circ$.

Calculate the length, in cm to 3 significant figures, of BC.

Diagram NOT accurately drawn.

The diagram shows the right-angled triangle ABC.
$AB=20\text{ cm}$, $BC=42.5\text{ cm}$ and $\angle BAC=90^\circ$.
Calculate the length of AC.

The diagram shows a quadrilateral ABCD in which
$$BC=25\text{ cm}\qquad AB=50\text{ cm}\qquad CD=35\text{ cm}\qquad \angle BAD=\angle CDA=90^\circ.$$
Calculate the perimeter, in cm, of quadrilateral ABCD.

Diagram NOT accurately drawn.

Figure 1 shows a framework of wooden beams, with ADC a straight line.
$$AB=8\text{ m},\quad BC=3.5\text{ m},\quad BD=2.5\text{ m},\quad \angle ADB=90^\circ.$$

Calculate, giving your answer to the nearest metre, the length of AC

Diagram NOT accurately drawn

The diagram shows quadrilateral ABCD.
$$AD=BC=(x-4)\text{ cm}$$$$DC=AB=(2x+3)\text{ cm}$$$$AC=\sqrt{5x^2+4x+25}\text{ cm}$$

Using algebra, show that ABCD is a rectangle.

ABCD is a rectangle with perimeter 28 m.
The length of AB is 8 m.
Calculate the length, in m, of the diagonal AC of the rectangle.

The diagram shows a prism ABCDEF.

BCFE is a rectangle and ABC and DEF are congruent triangles.
CF=DE=40 cm, EF=DC=AB=100 cm, $\angle FBC=30^\circ$.

H is the point on BF such that BH=57.5 cm.

Calculate EH.

A rhombus has diagonals of length 10 cm and 24 cm .

Find the perimeter of the rhombus.

The points A and B are such that the coordinates of A are (3,-2) and
$$\overrightarrow{BA}=\binom{-1}{4}.$$

The point C has coordinates (m,n), where m>3.
Given that $|\overrightarrow{AC}|=5$, find an expression for m in terms of n.
m=

ABCD is a kite so that the points A, B, C and D lie on a circle with radius 7.5 cm. The diagonals, AC and BD, of the kite intersect at point E, so that $A E=3 \mathrm{~cm}$. The line AEC is a diameter of the circle.

Find the area of the kite ABCD