Class 9 Practice – Level 1 – Areas of Parallelograms and Triangles Leave a Comment / By Gulam Hamza / September 14, 2024 Class 9 Practice – Level 1 – Areas of Parallelograms and Triangles Total questions: 40 1. n figure, PSDA is a parallelogram. Points Q and R are taken on PS such that PQ = QR = RS and PA || QB || RC. Prove that ar (PQE) = ar (CFD). △PQE≅△CPD △PCE≅△CFD △PFE≅△CFD △PQE≅△CFD None 2. If E, F, G and H are respectively the mid-points of the sides of a parallelogram ABCD, then ar(EFGH)=$\displaystyle \dfrac{1}{2}$ ar(ABCD) True False None 3. The median of a triangle divides it into two triangles of equal areas. False True None 4. PQRS is a square. T and U are respectively, the mid-points of PS and QR (Fig.). Find the area of ∆OTS, if PQ = 8 cm, where O is the point of intersection of TU and QS. 8 cm² 4 cm² 6 cm² 10 cm² None 5. The base BC of ΔABC is divided at D, such that BD= $\displaystyle \dfrac{1}{2}$ DC. Prove that ar(ΔABD)= $\displaystyle \dfrac{1}{3}$ ar(ΔABC) ar(△ABD)=ar(△ADE)=ar(△AEC)= $\displaystyle \dfrac{1}{3}$ ar(△ABC). ar(△AED)=ar(△ADE)=ar(△ABC)= $\displaystyle \dfrac{1}{3}$ ar(△ABC). ar(△ABD)=ar(△ADE)=ar(△AEC)= $\displaystyle \dfrac{1}{6}$ ar(△ABC). ar(△ABD)=ar(△ADE)=ar(△AEC)= $\displaystyle \dfrac{2}{5}$ ar(△ABC). None 6. In figure, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. then (i) ar (ACB) = ar (ACF) (ii) ar (AEDF) = ar (ABCDE) ar(PQRST) ar(GHIJK) None of these ar(ABCDE) None 7. In ABCD is a parallelogram and EFCD is a rectangle. Also, AL⊥DC. then (i) ar (ABCD) = ar (EFCD)(ii) ar (ABCD) = DC × AL True False None 8. ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ (Fig.). If AQ intersects DC at P, then ar (BPC) = ar (DPQ). Triangles On The Same Base And Between The Same Parallels False True None 9. ABCD is a parallelogram. E is a point on BA such that BE=2EA and F is a point on DC=2FC. Prove that AECF is a parallelogram whose area is one third of the area of parallelogram ABCD. True False None 10. P, Q, R, S are respectively the midpoints of the sides AB, BC, CD and DA of parallelogram ABCD. Show that PQRS is a parallelogram then ar(∥PQRS)= $\displaystyle \dfrac{1}{2}$ ar(∥ABCD) True False None 11. In the figure, area △ABC=27 cm² and EF∥BC. Find area of ∥ m ABCF. 54 cm² 44 cm² 58 cm² 89 cm² None 12. X and Y are respectively two points on the sides DC and AD of the parallelogram ABCD. The area of △ABX is equal to k times area of △BYC. 0 1 0.5 4 None 13. In a parallelogram ABCD, AB = 8 cm. The altitudes corresponding to sides AB and AD are respectively 4 cm and 5 cm. Find AD. 6.4 cm 3.4 cm 6.8 cm 7.5 cm None 14. In the given figure, ABCD is rectangle with AB = 5 cm, and BC = 3 cm. Find the area of the parallelogram ABEF. 10 cm² 14 cm² 15 cm² 35 cm² None 15. ABCD is a parallelogram in which AB || CD and AB = CD = 10 cm. If the perpendicular distance between AB and CD be 8 cm, find the area of the parallelogram ABCD 80 cm² 40 cm² 10 cm² 120cm² None 16. ABCD is a parallelogram having area 240 cm 2 ,BC=AD=20 cm and BC∥AD, Find the distance between the parallel sides BC and AD. 6 cm 8 cm 32 cm 12 cm None 17. ABCD is a parallelogram having area 160 cm 2 ,BC∥AD and the perpendicular distance between BC and AD is 10 cm. Find the length of the side BC. 4 cm 8 cm 16 cm 14 cm None 18. ABCD is a parallelogram having area 200 cm² . If AB∥CD pints P and Q divide AB and DC respectively, find the area of the parallelogram APQD. 100 cm² 50 cm² 25 cm² 200cm² None 19. ABCD is a parallelogram having area 450 cm². If AB∥CD points P and Q divide AB and DC respectively in the ratio 1:2 find the area of the parallelogram PBCQ. 450 cm² 150 cm² 300 cm² 100 cm² None 20. In fig ABCD is a trapezium in which AB= 7 cm, AD = BC = 5 cm. DC = x cm, and distance between AB and DC is 4 cm.Find the value of x and area of trapezium ABCD. 10 cm 12 cm 13 cm 20 cm None 21. ABCD is a rectangle, ABEF is a parallelogram with area of 30 cm 2 and AB and CF are parallel. Find area of rectangle ABCD 90 cm² 80 cm² 30 cm² 40 cm² None 22. Find the area of the quadrilateral whose Base is 5 m and Height is 4 m. 12 m² 18 m² 20 m² 14 m² None 23. If the ratio of the altitude and the area of the parallelogram is 2:11, then find the base of the parallelogram. 4.8 2.8 5.5 3.8 None 24. A diagonal of a parallelogram divides into .........triangles of equal area. 4 3 2 1 None 25. In a parallelogram PQRS, PS = 12. The altitude to side PS is equal to 12cm. Find area of parallelogram PQRS. 36 sq. cm 216 sq. cm 112 sq. cm 144 sq. cm None 26. ABCD is a parallelogram and Q is any point on side AD. If ar(△QBC)=10 cm² , find ar(△QAB)+ar(△QDC). 5 cm² 10 cm² 20 cm² 25 cm² None 27. In the given figure △ABC is right angled at B in which BC=15 cm, and CA=17 cm. Find the area of acute-angled triangle △DBC, it being given that AD∥BC. 20 cm² 60 cm² 40 cm² 50 cm² None 28. Triangles having the same base have equal area. TRUE FALSE Sometimes true can't say None 29. Check the given diagram and choose the correct answer ar(△ABC)=ar(△ADB)+2ar(△ACD) ar(△ABC)=ar(△ADB)+ar(△ACD) ar(△ABC)=ar(△ADB)−ar(△ACD) ar(△ABC)=ar(△ADB)×ar(△ACD) None 30. The △ABC and △EBC both have common base BC, then the area of △ABC is ..........the area of △EBD. equal to thrice not equal to none of these None 31. The perimeter of an equilateral triangle is 21 yard. What is the length of its each side? 14 yard 7 yard 8 yard 12 yard None 32. If L be any Point on AB and the area of rectangle ABCD is 100 square cm. find area of △LCD 200 sq. cm 150 sq. cm 50 sq. cm 100 sq. cm None 33. In the given figure, area (parallelogram ABCD)=48 cm² and FC∥AB. Find area of ∥gm ABEF. 12 cm² 24 cm² 48 cm² 18 cm² None 34. P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. If ar(APB)=kar(BQC), find k. 1 2 0.5 4 None 35. Two parallelograms are on the same base and between the same parallels. The ratio of their areas is : 1:4 1:2 1:1 1:3 None 36. A parallelogram and a square are on equal base and between the same parallel lines. Then the ratio of their areas is 1:1 2:1 1:1 1:4 None 37. A rectangle and a rhombus are on the same base and between the same parallels. The ratio of their areas is : 1:2 1:1 1:3 1:4 None 38. In △ABC if D is a point in BC and divides it in the ratio 3:5 i.e. if BD:DC=3:5 then ar (△ADC):ar(△ABC)= 3 : 5 3 : 8 5 : 8 8 : 3 None 39. From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is 60 cm² 90 cm² 30 cm² 40 cm² None 40. If heights of two triangles are in the ratio 4:9 then find the ratio of their areas. 9 : 4 17: 21 2 : 3 8 : 9 None 1 out of 40 Time's up
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