The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper SUVX that measures 22 cm by 12 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 74°. Find ∠TWV in Figure 2.
(a)
Area of Rectangle SUVX
= 22 x 12
= 264
Area of Triangle STX
=
12 x 5 x 12
= 30 cm
2 Area of Triangle TXW
= (264 - 30 - 30) ÷ 2
= 204 ÷ 2
= 102 cm
2 Area of STWVX
= 102 + 30 + 30
= 162 cm
2 (b)
∠XTW
= (180° - 74°) ÷ 2
= 106 ÷ 2
= 53° (Angles on a straight line)
∠TWV
= 360° - 90° - 90° - 53°
= 127° (Sum of angles in a quadrilateral)
Answer(s): (a) 162 cm
2; (b) 127°