Worksheet on same base and same parallels will help us to practice the different types of questions on area proportions.

**1.** Parallelogram PQRS and rectangle PQUT are on the same base PQ and between the same parallels PQ and TR. Also, the area of the parallelogram is 63 cm^2 and the width of the
rectangle is 9 cm. Find the length of the rectangle and its area.

**2.** In the adjoining
figure, ∆PQR is right angled at Q in which QR = 6 cm and PQ = 7 cm. Find the
area of ∆QSR; given that PS∥QR.

**3. **Parallelogram PQRS and PQTU are on the same base PQ and between same parallels PQ and UR. Area
of parallelogram PQRS = 56 cm^2 and the altitude of the parallelogram PQTU = 7
cm. Find the length of the common side of two parallelograms.

**4.** Parallelogram PQRS, ∆PQS, and rectangle PQTU have the same base PQ. If the area of ∆PSQ = 48
cm^2, then find the area of parallelogram PQRS and the area of rectangle PQTU.

**5.** LM is median
of ∆JKL, JK = 10 cm and the altitude of the ∆JKL = 4 cm, find the area of ∆JLM
and area of ∆LMK

**6.** AD is the
median of ∆ABC. E is any point on AD. Show that area of ∆ABE = area of ∆ACE

**7.** The diagonal of the quadrilateral ABCD, (DB, AC) intersect
at O. If OB = OD, then show that ∆ABC and ∆ADC have same areas.

[**Hint:** AO is the median of ∆ADB. Find
area of triangles AOD and AOB …………… (1)

OC is the median ∆DCB. Find areas of triangles DOC and BOC …………… (2)

Add (1) and (2)].

**8.** In the parallelogram ABCD, E, F
are any two points on sides AB and BC respectively. Show that ∆DFA and ∆DEC
have same areas.

**9.** ∆PQR is isosceles triangle with ST//QR. The medians SR and QT intersect each other at O.

Prove that area of (1) ∆QTS = ∆RST

(2) ∆QOS = ∆ROT

(3) ∆PQT = ∆PRS

Answers for the worksheet on same base and same parallels are given below to check the exact answer.

**Answers:**

**1.** Length = 7 cm,
Area = 63 cm^2

**2.** Area = 21 cm^2

**3.** Length = 8 cm

**4.** Area = 96 cm^2

**5.** Area = 10 cm^2

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