The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper GJKM that measures 18 cm by 13 cm. GH = LK = 5 cm. The paper is folded along the dotted line HL such that point J touches point M, as shown in Figure 2.
- Find the area of Figure 2. GHLKM, after the folding.
- In Figure 2, ∠GHM is 76°. Find ∠HLK in Figure 2.
(a)
Area of Rectangle GJKM
= 18 x 13
= 234
Area of Triangle GHM
=
12 x 5 x 13
= 32.5 cm
2 Area of Triangle HML
= (234 - 32.5 - 32.5) ÷ 2
= 169 ÷ 2
= 84.5 cm
2 Area of GHLKM
= 84.5 + 32.5 + 32.5
= 149.5 cm
2 (b)
∠MHL
= (180° - 76°) ÷ 2
= 104 ÷ 2
= 52° (Angles on a straight line)
∠HLK
= 360° - 90° - 90° - 52°
= 128° (Sum of angles in a quadrilateral)
Answer(s): (a) 149.5 cm
2; (b) 128°