The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper FHJL that measures 18 cm by 16 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 78°. Find ∠GKJ in Figure 2.
(a)
Area of Rectangle FHJL
= 18 x 16
= 288
Area of Triangle FGL
=
12 x 6 x 16
= 48 cm
2 Area of Triangle GLK
= (288 - 48 - 48) ÷ 2
= 192 ÷ 2
= 96 cm
2 Area of FGKJL
= 96 + 48 + 48
= 192 cm
2 (b)
∠LGK
= (180° - 78°) ÷ 2
= 102 ÷ 2
= 51° (Angles on a straight line)
∠GKJ
= 360° - 90° - 90° - 51°
= 129° (Sum of angles in a quadrilateral)
Answer(s): (a) 192 cm
2; (b) 129°