Class 9 Areas — Figures on the Same Base — practice questions with answers
Geometry · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. Two figures are said to be on the same base and between the same parallels if they have a common base and their other vertices lie on a line parallel to the base. Such parallelograms have areas that are:
Aequal
Bin the ratio 1:2
Calways unequal
Din the ratio 2:1
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Answer: A) equal
Parallelograms on the same base and between the same parallels are equal in area (a basic theorem of Class 9).
2. Triangle ABC has area 60 cm². AD is the median to BC. Find ar(ABD) in cm².
A33
B27
C60
D30
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Answer: D) 30
A median divides the triangle into two equal areas, so ar(ABD) = 21(60) = 30 cm².
3. Farmer Ramesh has a triangular field ABC of area 4800 m². He draws the median AD to fence off plot ABD for wheat. The area of the wheat plot (in m²) is:
A2160
B2400
C4800
D2640
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Answer: B) 2400
The median AD divides triangle ABC into two equal-area parts, so the wheat plot ABD = 4800 / 2 = 2400 m².
4. Triangles ABD and ACD lie on the same base AD. B and C are on opposite sides of line AD, each at perpendicular distance 5 cm from AD, and AD = 8 cm. The total area of quadrilateral ABDC (in cm²) is:
A44
B80
C40
D36
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Answer: C) 40
Each triangle = 21(8)(5) = 20 cm². They are on opposite sides of AD, so total area = 20 + 20 = 40 cm².
5. In quadrilateral ABCD, the diagonal AC is drawn. A line through B parallel to AC meets DC extended at E. By the same-base theorem, ar(triangle ACE) equals ar(triangle ACB) because:
Aboth are on base AC between the same parallels AC and BE
Bthey are congruent
CAC bisects the quadrilateral
DBE is perpendicular to AC
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Answer: A) both are on base AC between the same parallels AC and BE
B and E lie on the line BE which is parallel to AC, so triangles ACB and ACE share base AC and lie between the same parallels, giving equal areas. (This is the standard 'replace a quadrilateral by an equal-area triangle' construction.)