The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper KMNQ that measures 21 cm by 13 cm. KL = PN = 6 cm. The paper is folded along the dotted line LP such that point M touches point Q, as shown in Figure 2.
- Find the area of Figure 2. KLPNQ, after the folding.
- In Figure 2, ∠KLQ is 73°. Find ∠LPN in Figure 2.
(a)
Area of Rectangle KMNQ
= 21 x 13
= 273
Area of Triangle KLQ
=
12 x 6 x 13
= 39 cm
2 Area of Triangle LQP
= (273 - 39 - 39) ÷ 2
= 195 ÷ 2
= 97.5 cm
2 Area of KLPNQ
= 97.5 + 39 + 39
= 175.5 cm
2 (b)
∠QLP
= (180° - 73°) ÷ 2
= 107 ÷ 2
= 53.5° (Angles on a straight line)
∠LPN
= 360° - 90° - 90° - 53.5°
= 126.5° (Sum of angles in a quadrilateral)
Answer(s): (a) 175.5 cm
2; (b) 126.5°