The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper FHJL that measures 18 cm by 13 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 75°. Find ∠GKJ in Figure 2.
(a)
Area of Rectangle FHJL
= 18 x 13
= 234
Area of Triangle FGL
=
12 x 6 x 13
= 39 cm
2 Area of Triangle GLK
= (234 - 39 - 39) ÷ 2
= 156 ÷ 2
= 78 cm
2 Area of FGKJL
= 78 + 39 + 39
= 156 cm
2 (b)
∠LGK
= (180° - 75°) ÷ 2
= 105 ÷ 2
= 52.5° (Angles on a straight line)
∠GKJ
= 360° - 90° - 90° - 52.5°
= 127.5° (Sum of angles in a quadrilateral)
Answer(s): (a) 156 cm
2; (b) 127.5°