Shape and Space 4

In a quadrilateral ABCD, angles ABC and CDA are right angles. AB = 9 cm, BC = 5 cm, and CD = 7 cm. Describe how you would calculate the area of quadrilateral ABCD.

A road rises from a point A to a point B at a constant angle of 6° above the horizontal. The horizontal distance from A to B is 120 m. Calculate the vertical height gained between A and B.

The triangle PQR is right-angled at Q. PQ = 8.0 cm and QR = 6.0 cm.

A rectangle has a diagonal of length 25 m and one of its sides is 24 m. Find the length of the other side.

The diagram shows a right-angled triangle XYZ where Y is the right angle, XY = 7.8 cm and angle ZXY = 38°.

A ship is sailing directly towards a lighthouse. From one point at sea, the angle of elevation from the ship to the top of the lighthouse is 14°. After the ship sails 200 metres closer to the lighthouse in a straight line, the angle of elevation increases to 22°. The height of the lighthouse is h metres.

Calculate the height h of the lighthouse.

Give your answer correct to 3 significant figures.

Explain, with reference to the properties of parallelograms and right triangles, how you can use Pythagoras’ theorem to prove that the diagonals of a rhombus are perpendicular.

Write your answer in full sentences.

The diagram below shows quadrilateral ABCD with AB = AD = 10 cm, BC = CD = 7 cm, and angle BAD = 120°.

Calculate: