The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper HKLN that measures 22 cm by 16 cm. HJ = ML = 6 cm. The paper is folded along the dotted line JM such that point K touches point N, as shown in Figure 2.
- Find the area of Figure 2. HJMLN, after the folding.
- In Figure 2, ∠HJN is 75°. Find ∠JML in Figure 2.
(a)
Area of Rectangle HKLN
= 22 x 16
= 352
Area of Triangle HJN
=
12 x 6 x 16
= 48 cm
2 Area of Triangle JNM
= (352 - 48 - 48) ÷ 2
= 256 ÷ 2
= 128 cm
2 Area of HJMLN
= 128 + 48 + 48
= 224 cm
2 (b)
∠NJM
= (180° - 75°) ÷ 2
= 105 ÷ 2
= 52.5° (Angles on a straight line)
∠JML
= 360° - 90° - 90° - 52.5°
= 127.5° (Sum of angles in a quadrilateral)
Answer(s): (a) 224 cm
2; (b) 127.5°