Question 4
(4) The figure above shows an irregular quadrilateral:
(a) copy, full size, the given view;
(b) (i) construct a square twice in area of the quadrilateral;
(ii) measure and state the length of the square.
Observation
Candidates were expected to:
A. COPY THE GIVEN VIEW
- draw the base PQ;
- draw PS at 105O to PQ;
- locate point R and complete the quadrilateral PQRS.
B. CONVERT TO TRIANGLE
- produce PQ to a reasonable length;
- join SQ and RT parallel to SQ;
- complete triangle PTS.
C CONVERT TO RECTANGLE
- drop perpendicular from S to V and bisect SV;
- draw rectangle PTMN.
D. CONVERT TO SQUARE
- draw TL = TM;
- bisect PL and draw semi-circle on PL;
- produce TM to F and draw square TFGH.
E. ENLARGE SQUARE
Alternative A
- join FH;
- draw perpendiculars from H and F;
- complete the square FHJK.
OR
Alternative B
- draw perpendicular for H and make HD = HT;
- use T as centre and radius TD intercept PT produced at C;
- complete the square TABC.
F. (i) use correct scale 1:1;
(ii) measure and state the length = 58 ± 1;
(iii) draw neatly.
The solution is shown below.
SIMILAR AREAS AND ENLARGEMENT
LENGTH OF SIDE OF ENLARGED SQUARE = 58mm ± 1