# GMAT Quant | Geometry & Solid Geometry

Practice Questions in Geometry & Mensuration

You may get three to five questions from Geometry and Solid Geometry in the GMAT quant section - in both variants viz., problem solving and data sufficiency. The concepts tested include lines, angles, triangles, quadrilaterals, circles, coordinate geometry, solid geometry, finding the area, perimeter of two dimensional geometric shapes and surface area, volume, longest diagnal of solids including cones, cylinders, cube, rectangular cube, sphere, and hemisphere.

Sample GMAT practice questions from Geometry is given below. Attempt these questions and check whether you have got the correct answer. If you could not get the answer, go to the explanatory answer or the video explanations (wherever provided) to learn how to solve the question.

1. Vertices of a quadrilateral ABCD are A(0, 0), B(4, 5), C(9, 9) and D(5, 4). What is the shape of the quadrilateral?

1. Square
2. Rectangle but not a square
3. Rhombus
4. Parallelogram but not a rhombus
5. Kite
2. What is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between the two sides is 150o?

1. 24 sq units
2. 48 sq units
3. ${24}{$sqrt {3}}$ 4. ${48}{\sqrt {3}}$ 5. Such a triangle does not exist 3. What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40 and 41? 1. 6 2. 4 3. 24.5 4. 20.5 5. 12.5 4. If the sum of the interior angles of a regular polygon measures 1440o, how many sides does the polygon have? 1. 10 sides 2. 8 sides 3. 12 sides 4. 9 sides 5. None of these 5. What is the radius of the incircle of the triangle whose sides measure 5, 12 and 13 units? 1. 2 units 2. 12 units 3. 6.5 units 4. 6 units 5. 7.5 units 6. How many diagonals does a 63-sided convex polygon have? 1. 3780 2. 1890 3. 3843 4. 3906 5. 1953 7. If 10, 12 and 'x' are sides of an acute angled triangle, how many integer values of 'x' are possible? 1. 7 2. 12 3. 9 4. 13 5. 11 8. Data Sufficiency :Is triangle ABC obtuse angled? 1. a2 + b2 > c2. 2. The center of the circle circumscribing the triangle does not lie inside the triangle. 9. Data Sufficiency :Is triangle ABC with sides a, b and c acute angled? 1. Triangle with sides a2, b2, c2 has an area of 140 sq cms. 2. Median AD to side BC is equal to altitude AE to side BC. 10. A cube of side 5 cm is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted? 1. 9 2. 61 3. 98 4. 54 5. 64 11. A wheel of a car of radius 21 cms is rotating at 600 RPM. What is the speed of the car in km/hr? 1. 79.2 km/hr 2. 47.52 km/hr 3. 7.92 km/hr 4. 39.6 km/hr 5. 3.96 km/hr 12. The area of a square field is 24200 sq m. How long will a lady take to cross the field diagonally at the rate of 6.6 km/hr? 1. 3 minutes 2. 0.04 hours 3. 2 minutes 4. 2.4 minutes 5. 2 minutes 40 seconds 13. A lady grows cabbage in her garden that is in the shape of a square. Each cabbage takes 1 square foot of area in her garden. This year, she has increased her output by 211 cabbages when compared to last year. The shape of the area used for growing the cabbage has remained a square in both these years. How many cabbages did she produce this year? 1. 11236 2. 11025 3. 14400 4. 12696 5. Cannot be determined 14. The length of a rope, to which a cow is tied, is increased from 19 m to 30 m. How much additional ground will it be able to graze? Assume that the cow is able to move on all sides with equal ease. Use π = \\frac{22}{7}\\$ in your calculations.

1. 1696 sq m
2. 1694 sq m
3. 1594 sq m
4. 1756 sq.m
5. 1896 sq.m

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