The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper MPQS that measures 21 cm by 14 cm. MN = RQ = 6 cm. The paper is folded along the dotted line NR such that point P touches point S, as shown in Figure 2.
- Find the area of Figure 2. MNRQS, after the folding.
- In Figure 2, ∠MNS is 73°. Find ∠NRQ in Figure 2.
(a)
Area of Rectangle MPQS
= 21 x 14
= 294
Area of Triangle MNS
=
12 x 6 x 14
= 42 cm
2 Area of Triangle NSR
= (294 - 42 - 42) ÷ 2
= 210 ÷ 2
= 105 cm
2 Area of MNRQS
= 105 + 42 + 42
= 189 cm
2 (b)
∠SNR
= (180° - 73°) ÷ 2
= 107 ÷ 2
= 53.5° (Angles on a straight line)
∠NRQ
= 360° - 90° - 90° - 53.5°
= 126.5° (Sum of angles in a quadrilateral)
Answer(s): (a) 189 cm
2; (b) 126.5°