The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper KMNQ that measures 22 cm by 16 cm. KL = PN = 5 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 72°. Find ∠LPN in Figure 2.
(a)
Area of Rectangle KMNQ
= 22 x 16
= 352
Area of Triangle KLQ
=
12 x 5 x 16
= 40 cm
2 Area of Triangle LQP
= (352 - 40 - 40) ÷ 2
= 272 ÷ 2
= 136 cm
2 Area of KLPNQ
= 136 + 40 + 40
= 216 cm
2 (b)
∠QLP
= (180° - 72°) ÷ 2
= 108 ÷ 2
= 54° (Angles on a straight line)
∠LPN
= 360° - 90° - 90° - 54°
= 126° (Sum of angles in a quadrilateral)
Answer(s): (a) 216 cm
2; (b) 126°