The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper MPQS that measures 20 cm by 13 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 77°. Find ∠NRQ in Figure 2.
(a)
Area of Rectangle MPQS
= 20 x 13
= 260
Area of Triangle MNS
=
12 x 6 x 13
= 39 cm
2 Area of Triangle NSR
= (260 - 39 - 39) ÷ 2
= 182 ÷ 2
= 91 cm
2 Area of MNRQS
= 91 + 39 + 39
= 169 cm
2 (b)
∠SNR
= (180° - 77°) ÷ 2
= 103 ÷ 2
= 51.5° (Angles on a straight line)
∠NRQ
= 360° - 90° - 90° - 51.5°
= 128.5° (Sum of angles in a quadrilateral)
Answer(s): (a) 169 cm
2; (b) 128.5°