The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper LNPR that measures 19 cm by 16 cm. LM = QP = 5 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 76°. Find ∠MQP in Figure 2.
(a)
Area of Rectangle LNPR
= 19 x 16
= 304
Area of Triangle LMR
=
12 x 5 x 16
= 40 cm
2 Area of Triangle MRQ
= (304 - 40 - 40) ÷ 2
= 224 ÷ 2
= 112 cm
2 Area of LMQPR
= 112 + 40 + 40
= 192 cm
2 (b)
∠RMQ
= (180° - 76°) ÷ 2
= 104 ÷ 2
= 52° (Angles on a straight line)
∠MQP
= 360° - 90° - 90° - 52°
= 128° (Sum of angles in a quadrilateral)
Answer(s): (a) 192 cm
2; (b) 128°