The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper FHJL that measures 19 cm by 12 cm. FG = KJ = 6 cm. The paper is folded along the dotted line GK such that point H touches point L, as shown in Figure 2.
- Find the area of Figure 2. FGKJL, after the folding.
- In Figure 2, ∠FGL is 79°. Find ∠GKJ in Figure 2.
(a)
Area of Rectangle FHJL
= 19 x 12
= 228
Area of Triangle FGL
=
12 x 6 x 12
= 36 cm
2 Area of Triangle GLK
= (228 - 36 - 36) ÷ 2
= 156 ÷ 2
= 78 cm
2 Area of FGKJL
= 78 + 36 + 36
= 150 cm
2 (b)
∠LGK
= (180° - 79°) ÷ 2
= 101 ÷ 2
= 50.5° (Angles on a straight line)
∠GKJ
= 360° - 90° - 90° - 50.5°
= 129.5° (Sum of angles in a quadrilateral)
Answer(s): (a) 150 cm
2; (b) 129.5°