The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper LNPR that measures 19 cm by 12 cm. LM = QP = 6 cm. The paper is folded along the dotted line MQ such that point N touches point R, as shown in Figure 2.
- Find the area of Figure 2. LMQPR, after the folding.
- In Figure 2, ∠LMR is 73°. Find ∠MQP in Figure 2.
(a)
Area of Rectangle LNPR
= 19 x 12
= 228
Area of Triangle LMR
=
12 x 6 x 12
= 36 cm
2 Area of Triangle MRQ
= (228 - 36 - 36) ÷ 2
= 156 ÷ 2
= 78 cm
2 Area of LMQPR
= 78 + 36 + 36
= 150 cm
2 (b)
∠RMQ
= (180° - 73°) ÷ 2
= 107 ÷ 2
= 53.5° (Angles on a straight line)
∠MQP
= 360° - 90° - 90° - 53.5°
= 126.5° (Sum of angles in a quadrilateral)
Answer(s): (a) 150 cm
2; (b) 126.5°