The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper TVWY that measures 21 cm by 13 cm. TU = XW = 4 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 77°. Find ∠UXW in Figure 2.
(a)
Area of Rectangle TVWY
= 21 x 13
= 273
Area of Triangle TUY
=
12 x 4 x 13
= 26 cm
2 Area of Triangle UYX
= (273 - 26 - 26) ÷ 2
= 221 ÷ 2
= 110.5 cm
2 Area of TUXWY
= 110.5 + 26 + 26
= 162.5 cm
2 (b)
∠YUX
= (180° - 77°) ÷ 2
= 103 ÷ 2
= 51.5° (Angles on a straight line)
∠UXW
= 360° - 90° - 90° - 51.5°
= 128.5° (Sum of angles in a quadrilateral)
Answer(s): (a) 162.5 cm
2; (b) 128.5°