The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper BDEG that measures 20 cm by 13 cm. BC = FE = 4 cm. The paper is folded along the dotted line CF such that point D touches point G, as shown in Figure 2.
- Find the area of Figure 2. BCFEG, after the folding.
- In Figure 2, ∠BCG is 73°. Find ∠CFE in Figure 2.
(a)
Area of Rectangle BDEG
= 20 x 13
= 260
Area of Triangle BCG
=
12 x 4 x 13
= 26 cm
2 Area of Triangle CGF
= (260 - 26 - 26) ÷ 2
= 208 ÷ 2
= 104 cm
2 Area of BCFEG
= 104 + 26 + 26
= 156 cm
2 (b)
∠GCF
= (180° - 73°) ÷ 2
= 107 ÷ 2
= 53.5° (Angles on a straight line)
∠CFE
= 360° - 90° - 90° - 53.5°
= 126.5° (Sum of angles in a quadrilateral)
Answer(s): (a) 156 cm
2; (b) 126.5°