q-8]A plastic box 1 5cmlong,1 25mwide and 65cm deep is to be made It is to be open at the - Maths - Surface Areas and Volumes

Question

q-8]A plastic box 1 5cmlong,1 25mwide and 65cm
deep is to be made It is to be open at the top Ignoring the
thickness if the plastic sheet, determine [1] the area of the sheet
required fo r making the box [2] the cost of sheet for it @costs Rs
20/m2

q-9] In triangle ABC,D are the mid point of AB
P is any on BC CQIIPD meets AB at Q show that area [triangle BPQ]
=1/2 area [triangle ABC]

q-10]PQRS is a llgm A is a any point on PS
such that PA=1/3PS and B is appoint on QR such that BR=1/2 QR prove
that PBRA is a llgm

Ajanta Trivedi · Accepted Answer

(1) the length of the plastic box l=1 5cm width of the plastic box b=1 25m=125cm depth of the plastic box h=65cm surface area of the 4 sides=2h(l+b)=2*65(1 5+125)=130*(126 5)=16445 cm square it is open at top therefore area of the base=lb=1 5*125=187 5 cm square total area of the sheet =16445+187 5=16632 5 cm square=1 66325 m square cost of the sheet =1 66325*20=33 27 /- (2)

given: D is the mid-point of BC and P is any point on AB and CQ is parallel to PD TPT: area [triangle BPQ] =1/2 area [triangle ABC] Proof: construction: join CD and PQ Î”PDQ and Î”PDC are on the same base PD and between same parallel lines PD and CQ therefore area(Î”PDQ) = area(Î”PDC) adding area of Î”BDP on both sides, we get area(Î”PDQ)+area(Î”BDP)=area(Î”PDC)+area(Î”BDP) area(Î”BPQ)=area(Î”BDC)=1/2 area(Î”ABC) [since AD is the median of triangle ABC and median divides the triangle into two equal areas] hence area(Î”BPQ)=1/2 area(Î”ABC) (3)

if the question is :PQRS is a llgm A is a any point on PS such that PA=1/3PS and B is appoint on QR such that BR=1/3 QR prove that PBRA is a llgm given: PQRS is a parallelogram and PA=1/3PS and BR=1/3QR TPT: PBRA is a parallelogram proof: since PQRS is a parallelogram $P S ∥ Q R a n d P S = Q R B R = \frac{1}{3} Q R = \frac{1}{3} P S \Rightarrow P A = B R a n d P A ∥ B R$ hence PABR is a parallelogram