The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper CEFH that measures 21 cm by 13 cm. CD = GF = 5 cm. The paper is folded along the dotted line DG such that point E touches point H, as shown in Figure 2.
- Find the area of Figure 2. CDGFH, after the folding.
- In Figure 2, ∠CDH is 72°. Find ∠DGF in Figure 2.
(a)
Area of Rectangle CEFH
= 21 x 13
= 273
Area of Triangle CDH
=
12 x 5 x 13
= 32.5 cm
2 Area of Triangle DHG
= (273 - 32.5 - 32.5) ÷ 2
= 208 ÷ 2
= 104 cm
2 Area of CDGFH
= 104 + 32.5 + 32.5
= 169 cm
2 (b)
∠HDG
= (180° - 72°) ÷ 2
= 108 ÷ 2
= 54° (Angles on a straight line)
∠DGF
= 360° - 90° - 90° - 54°
= 126° (Sum of angles in a quadrilateral)
Answer(s): (a) 169 cm
2; (b) 126°