The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper UWXZ that measures 19 cm by 13 cm. UV = YX = 4 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 73°. Find ∠VYX in Figure 2.
(a)
Area of Rectangle UWXZ
= 19 x 13
= 247
Area of Triangle UVZ
=
12 x 4 x 13
= 26 cm
2 Area of Triangle VZY
= (247 - 26 - 26) ÷ 2
= 195 ÷ 2
= 97.5 cm
2 Area of UVYXZ
= 97.5 + 26 + 26
= 149.5 cm
2 (b)
∠ZVY
= (180° - 73°) ÷ 2
= 107 ÷ 2
= 53.5° (Angles on a straight line)
∠VYX
= 360° - 90° - 90° - 53.5°
= 126.5° (Sum of angles in a quadrilateral)
Answer(s): (a) 149.5 cm
2; (b) 126.5°