The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper XZAC that measures 22 cm by 16 cm. XY = BA = 4 cm. The paper is folded along the dotted line YB such that point Z touches point C, as shown in Figure 2.
- Find the area of Figure 2. XYBAC, after the folding.
- In Figure 2, ∠XYC is 72°. Find ∠YBA in Figure 2.
(a)
Area of Rectangle XZAC
= 22 x 16
= 352
Area of Triangle XYC
=
12 x 4 x 16
= 32 cm
2 Area of Triangle YCB
= (352 - 32 - 32) ÷ 2
= 288 ÷ 2
= 144 cm
2 Area of XYBAC
= 144 + 32 + 32
= 208 cm
2 (b)
∠CYB
= (180° - 72°) ÷ 2
= 108 ÷ 2
= 54° (Angles on a straight line)
∠YBA
= 360° - 90° - 90° - 54°
= 126° (Sum of angles in a quadrilateral)
Answer(s): (a) 208 cm
2; (b) 126°