The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper NQRT that measures 22 cm by 14 cm. NP = SR = 5 cm. The paper is folded along the dotted line PS such that point Q touches point T, as shown in Figure 2.
- Find the area of Figure 2. NPSRT, after the folding.
- In Figure 2, ∠NPT is 75°. Find ∠PSR in Figure 2.
(a)
Area of Rectangle NQRT
= 22 x 14
= 308
Area of Triangle NPT
=
12 x 5 x 14
= 35 cm
2 Area of Triangle PTS
= (308 - 35 - 35) ÷ 2
= 238 ÷ 2
= 119 cm
2 Area of NPSRT
= 119 + 35 + 35
= 189 cm
2 (b)
∠TPS
= (180° - 75°) ÷ 2
= 105 ÷ 2
= 52.5° (Angles on a straight line)
∠PSR
= 360° - 90° - 90° - 52.5°
= 127.5° (Sum of angles in a quadrilateral)
Answer(s): (a) 189 cm
2; (b) 127.5°