The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper RTUW that measures 22 cm by 12 cm. RS = VU = 6 cm. The paper is folded along the dotted line SV such that point T touches point W, as shown in Figure 2.
- Find the area of Figure 2. RSVUW, after the folding.
- In Figure 2, ∠RSW is 74°. Find ∠SVU in Figure 2.
(a)
Area of Rectangle RTUW
= 22 x 12
= 264
Area of Triangle RSW
=
12 x 6 x 12
= 36 cm
2 Area of Triangle SWV
= (264 - 36 - 36) ÷ 2
= 192 ÷ 2
= 96 cm
2 Area of RSVUW
= 96 + 36 + 36
= 168 cm
2 (b)
∠WSV
= (180° - 74°) ÷ 2
= 106 ÷ 2
= 53° (Angles on a straight line)
∠SVU
= 360° - 90° - 90° - 53°
= 127° (Sum of angles in a quadrilateral)
Answer(s): (a) 168 cm
2; (b) 127°