The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper RTUW that measures 21 cm by 12 cm. RS = VU = 5 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 76°. Find ∠SVU in Figure 2.
(a)
Area of Rectangle RTUW
= 21 x 12
= 252
Area of Triangle RSW
=
12 x 5 x 12
= 30 cm
2 Area of Triangle SWV
= (252 - 30 - 30) ÷ 2
= 192 ÷ 2
= 96 cm
2 Area of RSVUW
= 96 + 30 + 30
= 156 cm
2 (b)
∠WSV
= (180° - 76°) ÷ 2
= 104 ÷ 2
= 52° (Angles on a straight line)
∠SVU
= 360° - 90° - 90° - 52°
= 128° (Sum of angles in a quadrilateral)
Answer(s): (a) 156 cm
2; (b) 128°