The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper BDEG that measures 19 cm by 13 cm. BC = FE = 6 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 78°. Find ∠CFE in Figure 2.
(a)
Area of Rectangle BDEG
= 19 x 13
= 247
Area of Triangle BCG
=
12 x 6 x 13
= 39 cm
2 Area of Triangle CGF
= (247 - 39 - 39) ÷ 2
= 169 ÷ 2
= 84.5 cm
2 Area of BCFEG
= 84.5 + 39 + 39
= 162.5 cm
2 (b)
∠GCF
= (180° - 78°) ÷ 2
= 102 ÷ 2
= 51° (Angles on a straight line)
∠CFE
= 360° - 90° - 90° - 51°
= 129° (Sum of angles in a quadrilateral)
Answer(s): (a) 162.5 cm
2; (b) 129°