The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper TVWY that measures 22 cm by 13 cm. TU = XW = 6 cm. The paper is folded along the dotted line UX such that point V touches point Y, as shown in Figure 2.
- Find the area of Figure 2. TUXWY, after the folding.
- In Figure 2, ∠TUY is 74°. Find ∠UXW in Figure 2.
(a)
Area of Rectangle TVWY
= 22 x 13
= 286
Area of Triangle TUY
=
12 x 6 x 13
= 39 cm
2 Area of Triangle UYX
= (286 - 39 - 39) ÷ 2
= 208 ÷ 2
= 104 cm
2 Area of TUXWY
= 104 + 39 + 39
= 182 cm
2 (b)
∠YUX
= (180° - 74°) ÷ 2
= 106 ÷ 2
= 53° (Angles on a straight line)
∠UXW
= 360° - 90° - 90° - 53°
= 127° (Sum of angles in a quadrilateral)
Answer(s): (a) 182 cm
2; (b) 127°