The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper TVWY that measures 18 cm by 12 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 79°. Find ∠UXW in Figure 2.
(a)
Area of Rectangle TVWY
= 18 x 12
= 216
Area of Triangle TUY
=
12 x 6 x 12
= 36 cm
2 Area of Triangle UYX
= (216 - 36 - 36) ÷ 2
= 144 ÷ 2
= 72 cm
2 Area of TUXWY
= 72 + 36 + 36
= 144 cm
2 (b)
∠YUX
= (180° - 79°) ÷ 2
= 101 ÷ 2
= 50.5° (Angles on a straight line)
∠UXW
= 360° - 90° - 90° - 50.5°
= 129.5° (Sum of angles in a quadrilateral)
Answer(s): (a) 144 cm
2; (b) 129.5°