The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper JLMP that measures 19 cm by 16 cm. JK = NM = 4 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
= 19 x 16
= 304
Area of Triangle JKP
=
12 x 4 x 16
= 32 cm
2 Area of Triangle KPN
= (304 - 32 - 32) ÷ 2
= 240 ÷ 2
= 120 cm
2 Area of JKNMP
= 120 + 32 + 32
= 184 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) 184 cm
2; (b) 127.5°