The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper UWXZ that measures 21 cm by 14 cm. UV = YX = 6 cm. The paper is folded along the dotted line VY such that point W touches point Z, as shown in Figure 2.
- Find the area of Figure 2. UVYXZ, after the folding.
- In Figure 2, ∠UVZ is 80°. Find ∠VYX in Figure 2.
(a)
Area of Rectangle UWXZ
= 21 x 14
= 294
Area of Triangle UVZ
=
12 x 6 x 14
= 42 cm
2 Area of Triangle VZY
= (294 - 42 - 42) ÷ 2
= 210 ÷ 2
= 105 cm
2 Area of UVYXZ
= 105 + 42 + 42
= 189 cm
2 (b)
∠ZVY
= (180° - 80°) ÷ 2
= 100 ÷ 2
= 50° (Angles on a straight line)
∠VYX
= 360° - 90° - 90° - 50°
= 130° (Sum of angles in a quadrilateral)
Answer(s): (a) 189 cm
2; (b) 130°