The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper JLMP that measures 20 cm by 12 cm. JK = NM = 5 cm. The paper is folded along the dotted line KN such that point L touches point P, as shown in Figure 2.
- Find the area of Figure 2. JKNMP, after the folding.
- In Figure 2, ∠JKP is 75°. Find ∠KNM in Figure 2.
(a)
Area of Rectangle JLMP
= 20 x 12
= 240
Area of Triangle JKP
=
12 x 5 x 12
= 30 cm
2 Area of Triangle KPN
= (240 - 30 - 30) ÷ 2
= 180 ÷ 2
= 90 cm
2 Area of JKNMP
= 90 + 30 + 30
= 150 cm
2 (b)
∠PKN
= (180° - 75°) ÷ 2
= 105 ÷ 2
= 52.5° (Angles on a straight line)
∠KNM
= 360° - 90° - 90° - 52.5°
= 127.5° (Sum of angles in a quadrilateral)
Answer(s): (a) 150 cm
2; (b) 127.5°