The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper SUVX that measures 22 cm by 16 cm. ST = WV = 5 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 78°. Find ∠TWV in Figure 2.
(a)
Area of Rectangle SUVX
= 22 x 16
= 352
Area of Triangle STX
=
12 x 5 x 16
= 40 cm
2 Area of Triangle TXW
= (352 - 40 - 40) ÷ 2
= 272 ÷ 2
= 136 cm
2 Area of STWVX
= 136 + 40 + 40
= 216 cm
2 (b)
∠XTW
= (180° - 78°) ÷ 2
= 102 ÷ 2
= 51° (Angles on a straight line)
∠TWV
= 360° - 90° - 90° - 51°
= 129° (Sum of angles in a quadrilateral)
Answer(s): (a) 216 cm
2; (b) 129°