The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper TVWY that measures 22 cm by 16 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 77°. Find ∠UXW in Figure 2.
(a)
Area of Rectangle TVWY
= 22 x 16
= 352
Area of Triangle TUY
=
12 x 6 x 16
= 48 cm
2 Area of Triangle UYX
= (352 - 48 - 48) ÷ 2
= 256 ÷ 2
= 128 cm
2 Area of TUXWY
= 128 + 48 + 48
= 224 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) 224 cm
2; (b) 128.5°