class 9 / maths

CLASS 9 / PRACTICE QUESTIONS

AREA OF PARALLELOGRAM AND TRIANGLE

Q.1) ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F.

 Show ar (∆ ACB) = ar(∆  ACF).

Q.2) In the given figure, PQR and QST are two triangles such that S is the mid-point of QR. and QT // PR.

Q.3) ABCD is a Quadrilateral. A line through D, parallel to AC, meets BC produced in P as shown in figure. Prove that ar(∆ ABP) = ar(Quad ABCD).

Q.4) In a triangle ABC, D is the mid-point of AB. P is any point of BC. CQ || PD meets AB in Q. Show that

Q.5) Prove that area (∆ AFG) = ½ area(BDEF).

Q.6) If D, E and F are the mid points of sides AB, BC and AC respectively then show that

(i) area (∆ ADE) = area (∆ AFE)

(ii) area (∆ BDE) = area (∆ CEF)

(iii) area (ADEF) = ½ area (∆ ABC)

Q7) In ∆ ABC, D is the mid-point of BC, E is the mid-point of BD. If „O‟ is the mid-point of AE, prove that

 ar (∆ BOE) = (1/8) ar (∆ ABC).

Q.8) In the given figure E is the midpoint of BC and D is the midpoint of AE. PEDB and QEDC are parallelograms then show that area (∆ PBE) + area (∆ QCE) = ½ area (∆ ABC).

Q.9) In the given figure, if BE||CF and area (ABCE) = area (BDEF) then prove that AD|| BE.

Q.10) The area of parallelogram PQRS is 152 cm². Find the area of rectangle PQXY. If the base PQ = 19 cm, find the height of the parallelogram.