SPM 2018 Add Maths Paper 2, Question 14Solution of Triangles

Solved on video in English and Bahasa Melayu · 10 marks · Form 4, Solution of Triangles · 8:06 video

The question

Solution by scale drawing is not accepted. Diagram 8 shows a transparent prism with a rectangular base ABCD. The inclined surface ABFE is a square with sides 12 cm and the inclined surface CDEF is a rectangle. AED is a uniform cross section of the prism. BDE is a blue coloured plane in the prism. It is given that angle ADE = 37° and angle EAD = 45°. Find (a) the length, in cm, of DE, (b) the area, in cm², of the blue coloured plane, (c) the shortest length, in cm, from point E to the straight line BD.

[10 marks]

SPM 2018 Add Maths Paper 2, Question 14: the question as drawn in Eduly's video

8:06

Step 1

EA is a side of the square face ABFE, so EA = 12 cm. In the cross-section triangle AED the known angles are angle EAD = 45° and angle ADE = 37°. By the sine rule, with DE opposite the 45° angle and EA opposite the 37° angle: DE / sin 45° = 12 / sin 37°.

Why this step

Each side pairs with the angle opposite it: DE faces 45°, EA faces 37°. Flipping the ratio gives about 10.2 cm, a common slip.

7 more steps, each with the reason for it, in the full solution

Final answer

(a) DE = 14.10 cm (b) 119.06 cm² (c) 10.31 cm

Where students lose marks

Watch out: only the sides of square ABFE are 12 cm. BE is its diagonal, 12√2, and DE comes from the sine rule.

Watch every step of this question solved on video (8:06), with the reason behind each step and a box that checks your own answer.

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SPM 2018 Add Maths Paper 2, Question 14Solution of Triangles

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