The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper MPQS that measures 21 cm by 13 cm. MN = RQ = 4 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 13
= 273
Area of Triangle MNS
=
12 x 4 x 13
= 26 cm
2 Area of Triangle NSR
= (273 - 26 - 26) ÷ 2
= 221 ÷ 2
= 110.5 cm
2 Area of MNRQS
= 110.5 + 26 + 26
= 162.5 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) 162.5 cm
2; (b) 126.5°