The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper SUVX that measures 21 cm by 16 cm. ST = WV = 6 cm. The paper is folded along the dotted line TW such that point U touches point X, as shown in Figure 2.
- Find the area of Figure 2. STWVX, after the folding.
- In Figure 2, ∠STX is 79°. Find ∠TWV in Figure 2.
(a)
Area of Rectangle SUVX
= 21 x 16
= 336
Area of Triangle STX
=
12 x 6 x 16
= 48 cm
2 Area of Triangle TXW
= (336 - 48 - 48) ÷ 2
= 240 ÷ 2
= 120 cm
2 Area of STWVX
= 120 + 48 + 48
= 216 cm
2 (b)
∠XTW
= (180° - 79°) ÷ 2
= 101 ÷ 2
= 50.5° (Angles on a straight line)
∠TWV
= 360° - 90° - 90° - 50.5°
= 129.5° (Sum of angles in a quadrilateral)
Answer(s): (a) 216 cm
2; (b) 129.5°