1. If the area of a triangle is 864 cm² and the ratio of its base to the corresponding altitude is 4 : 3, then the altitude of the triangle is:
(a) 18 cm
(b) 24 cm
(c) 27 cm
(d) 36 cm
2. The base of a triangle is 18 cm and its height is 10 cm. The height of another triangle of triple the area, having the base 15 cm, is:
(a) 18 cm
(b) 20 cm
(c) 24 cm
(d) 30 cm
3. The sides of a triangle are 6 cm, 8 cm, and 10 cm. The area (in cm²) of the triangle formed by joining the midpoints of its sides is:
(a) 6
(b) 12
(c) 18
(d) 24
4. The sides of a triangle are in the ratio 3 : 4 : 5. If the perimeter of the triangle is 24 cm, then the area (in cm²) of the triangle is:
(a) 24
(b) 36
(c) 48
(d) 60
5. The measures (in cm) of the sides of a right-angled triangle are given by three consecutive even integers. The area (in cm²) of the triangle is:
(a) 24
(b) 30
(c) 36
(d) 48
6. The lengths of the three medians of a triangle are 6 cm, 8 cm, and 10 cm. The area (in cm²) of the triangle is:
(a) 24
(b) 32
(c) 40
(d) 48
7. The ratio of the sides of a triangle is 3 : 4 : 5. If the area of the triangle is 96 square units, then the length of the smallest side is:
(a) 9 units
(b) 12 units
(c) 15 units
(d) 18 units
8. What is the area of a triangle having perimeter 30 cm, one side 10 cm, and the difference of the other two sides 2 cm?
(a) 12 cm²
(b) 16 cm²
(c) 24 cm²
(d) 30 cm²
9. The sides of a triangle are 9 cm, 12 cm, and 15 cm. Find the area of the triangle.
(a) 36 cm²
(b) 45 cm²
(c) 54 cm²
(d) 60 cm²
10. Two triangles △PQR and △XYZ are similar. If PQ=12 cm and XY=9 cm, then the ratio of the areas of triangles PQR and XYZ is:
(a) 3 : 2
(b) 4 : 3
(c) 16 : 9
(d) 9 : 16
11. If △PQR∼△XYZ such that QR=4 cm, YZ=6 cm and the area of △PQR is 64 cm², then the area of △XYZ is:
(a) 96 cm²
(b) 120 cm²
(c) 144 cm²
(d) 192 cm²
12. The areas of two similar triangles △PQR and △XYZ are 36 cm² and 64 cm² respectively. If PQ=6 cm, then the length of XY is:
(a) 8 cm
(b) 10 cm
(c) 12 cm
(d) 16 cm
13. In triangle ABC a line drawn parallel to base BC intersects AB and AC at points D and E respectively. If the area of △ABE is 25 cm², then the area of △ACD is:
(a) 20 cm²
(b) 25 cm²
(c) 30 cm²
(d) 50 cm²
14. The perimeter of a triangle is 24 m and its sides are in the ratio 3 : 4 : 5. The area of the triangle is:
(a) 18 m²
(b) 24 m²
(c) 30 m²
(d) 36 m²
15. If x and y are the lengths of the perpendicular sides of a right-angled triangle whose hypotenuse is 13 cm and whose area is 30 cm², then the value of (x + y)² is:
(a) 169
(b) 289
(c) 361
(d) 400
16. If the ratio of the altitudes of two triangles is 2 : 3 and the ratio of their corresponding areas is 8 : 9, then the ratio of their corresponding lengths of bases is:
(a) 3 : 4
(b) 4 : 3
(c) 4 : 5
(d) 6 : 5
17. The in-radius of a triangle is 5 cm, and the sum of the lengths of its sides is 36 cm. The area of the triangle (in square cm) is:
(a) 80
(b) 85
(c) 90
(d) 100
18. Two triangles △PQR and △XYZ are similar. If the ratio of their perimeters is 3 : 2, then the ratio of their areas is:
(a) 3 : 2
(b) 9 : 4
(c) 6 : 5
(d) 4 : 3
19. The hypotenuse of a right-angled triangle is 25 cm and the difference of the other two sides is 7 cm. Then, the area of the triangle is:
(a) 60 cm²
(b) 84 cm²
(c) 96 cm²
(d) 120 cm²
20. △PQR∼△XYZ. If the area of △PQR is 16 cm² and the area of △XYZ is 36 cm², and QR = 4 cm, then the length of YZ is:
(a) 5 cm
(b) 6 cm
(c) 8 cm
(d) 9 cm
21. In △PQR, points X and Y are the midpoints of PQ and PR respectively. The ratio of the areas of △PXY and quadrilateral QRYX is:
(a) 1 : 2
(b) 1 : 3
(c) 1 : 4
(d) 2 : 3
22. A string of length 40 cm is bent first into a square and then into a right-angled triangle, keeping one side of the square fixed as its base. The area of the triangle (in cm²) is:
(a) 40
(b) 48
(c) 60
(d) 80
23. The centroid of a triangle △PQR is G. If the area of △PQR is 90 sq. units, then the area of △QGR is:
(a) 20
(b) 25
(c) 30
(d) 45
24. In a triangle PQR, PQ=9 cm, PR=15 cm and ∠Q=90°. Then the area of △PQR is:
(a) 36 cm²
(b) 45 cm²
(c) 54 cm²
(d) 60 cm²
25. In a triangle ABC, a line DE is drawn parallel to BC intersecting AB and AC at D and E respectively. If DE=4 cm, BC=8 cm and the area of △ADE=20 sq. cm, then the area of △ABC is:
(a) 40 sq. cm
(b) 60 sq. cm
(c) 80 sq. cm
(d) 100 sq. cm
26. ∆PQR is similar to ∆XYZ. If the ratio of their corresponding sides is 3 : 2, then the ratio of their areas is:
(a) 3 : 2
(b) 9 : 4
(c) 6 : 4
(d) 3 : 4
27. The inradius of a triangle is 5 cm and its area is 60 sq. cm. The perimeter of the triangle is:
(a) 20 cm
(b) 22 cm
(c) 24 cm
(d) 26 cm
28. In △PQR, the medians PX and QY intersect at G. Find the ratio of the areas of △PGQ and the quadrilateral GXRY.
(a) 1 : 2
(b) 1 : 3
(c) 2 : 3
(d) 1 : 5
29. P, Q and R are the mid-points of the sides XY, YZ and ZX respectively of a triangle △XYZ. Then the ratio of the areas of △PQR and △XYZ is:
(a) 1 : 2
(b) 1 : 3
(c) 1 : 4
(d) 3 : 4
1. The radius of the incircle of a triangle is 3 cm. If the area of the triangle is 24 cm², then its perimeter is:
(a) 12 cm
(b) 14 cm
(c) 16 cm
(d) 18 cm
1. The sides of a triangular park are 9 m, 12 m and 15 m respectively. Find the cost of grassing the park at the rate of ₹4 per sq. m.
(a) ₹180
(b) ₹216
(c) ₹240
(d) ₹300
1. In an isosceles triangle, each of the equal sides is 13 cm and the angle between them is 60°. The area of the triangle is:
(a) 52 cm²
(b) 56 cm²
(c) 65 cm²
(d) 78 cm²
2. The area of the triangle formed by the straight line 4x+3y=12 and the coordinate axes is:
(a) 6 sq. units
(b) 9 sq. units
(c) 12 sq. units
(d) 18 sq. units
3. The area of an isosceles triangle is 12 square units. If the length of the base is 6 units, then the length of each equal side is:
(a) 4 units
(b) 5 units
(c) 6 units
(d) 7 units
4. A right-angled isosceles triangle is inscribed in a semi-circle of radius 14 cm such that the hypotenuse of the triangle is the diameter of the semi-circle. The area enclosed by the semi-circle but exterior to the triangle is:
(a) 154 cm²
(b) 112 cm²
(c) 462 cm²
(d) 616 cm²
5. The perimeter of an isosceles triangle is 300 cm. Each of the equal sides is 3/4 times the base. The area of the triangle (in cm²) is:
(a) 3600
(b) 4320
(c) 4800
(d) 5400
6. The altitude drawn to the base of an isosceles triangle is 6 cm and its perimeter is 48 cm. The area (in cm²) of the triangle is:
(a) 48
(b) 54
(c) 60
(d) 72
7. If the length of each of the two equal sides of an isosceles triangle is 13 cm and the adjacent (included) angle is 60°, then the area of the triangle is:
(a) 52 cm²
(b) 65 cm²
(c) 78 cm²
(d) 91 cm²
8. Two isosceles triangles have equal vertical angles. If the ratio of their areas is 4 : 25, then the ratio of their corresponding heights is:
(a) 2 : 5
(b) 4 : 5
(c) 5 : 4
(d) 16 : 25
9. The centroid of a triangle △PQR is G. If the area of △PQR is 90 cm², then the area of △GRQ is:
(a) 20 cm²
(b) 25 cm²
(c) 30 cm²
(d) 45 cm²
10. The ratio of the altitudes of two triangles is 3 : 4 and the ratio of their areas is 9 : 8. The ratio of their corresponding bases is:
(a) 3 : 2
(b) 4 : 3
(c) 8 : 9
(d) 9 : 8
1. The perimeter of a certain isosceles right-angled triangle is 24+12√2 cm. What is the length of the hypotenuse of the triangle?
(a) 12 cm
(b) 18 cm
(c) 24 cm
(d) 30 cm
2. In an isosceles triangle, the length of each equal side is 3 times the length of the third side. The ratio of the areas of this isosceles triangle and an equilateral triangle having the same perimeter is:
(a) 2 : 1
(b) 3 : 2
(c) 4 : 3
(d) 5 : 4
3. The lengths of two sides of an isosceles triangle are 10 cm and 18 cm respectively. What are the possible values of the perimeter of the triangle?
(a) 38 cm and 46 cm
(b) 38 cm and 48 cm
(c) 36 cm and 46 cm
(d) 40 cm and 46 cm
4. The ratio of the areas of two isosceles triangles having the same vertical angle (i.e., angle between the equal sides) is 9 : 16. The ratio of their heights is:
(a) 3 : 4
(b) 4 : 3
(c) 9 : 16
(d) 16 : 9
1. From a point inside an equilateral triangle, the lengths of the perpendiculars to its three sides are 4 cm, 5 cm and 7 cm respectively. The area of the triangle is:
(a) 48 cm²
(b) 54 cm²
(c) 60 cm²
(d) 72 cm²
2. The areas of two equilateral triangles are in the ratio 16 : 49. The ratio of their altitudes is:
(a) 4 : 7
(b) 7 : 4
(c) 16 : 49
(d) 8 : 14
3. XYZ is an equilateral triangle of side 4 cm. With X, Y, Z as centres and radius 2 cm, three arcs are drawn inside the triangle. The area of the region within the triangle but bounded by the three arcs is:
(a) 4π−4√3 cm²
(b) 8π−8√3 cm²
(c) 12π−8√3 cm²
(d) 16π−12√3 cm²
4. If the numerical value of the perimeter of an equilateral triangle is equal to twice the area of the triangle, then the length of each side of the triangle is:
(a) 2 units
(b) 3 units
(c) 4 units
(d) 6 units
5. Each side of an equilateral triangle is 8 cm. The area of the triangle is:
(a) 16√3 cm²
(b) 24√3 cm²
(c) 32√3 cm²
(d) 48√3 cm²
6. If the length of each side of an equilateral triangle is increased by 2 units, the area is found to be increased by 5√3 square units. The length of each side of the triangle is:
(a) 3 units
(b) 4 units
(c) 5 units
(d) 6 units
7. The height of an equilateral triangle is 12 cm. The area of the triangle is:
(a) 48√3 cm²
(b) 72√3 cm²
(c) 96√3 cm²
(d) 108√3 cm²
8. The area of an equilateral triangle is 12√3 m². The length (in m) of the median of the triangle is:
(a) 4
(b) 5
(c) 6
(d) 8
9. The length of a side of an equilateral triangle is 6 cm. The area of the region lying between the circumcircle and the incircle of the triangle is (Take π = 22/7):
(a) 44 cm²
(b) 55 cm²
(c) 66 cm²
(d) 77 cm²
10. The lengths of the perpendiculars from a point inside an equilateral triangle to its three sides are 4 cm, 5 cm and 7 cm respectively. The area of the triangle is:
(a) 48 cm²
(b) 60 cm²
(c) 72 cm²
(d) 84 cm²
11. The side of an equilateral triangle is 14 cm. Find the area (in cm²) of its incircle.
(a) 44
(b) 88
(c) 154
(d) 308
12. The side of an equilateral triangle is 12 cm. The ratio of the areas of its circumcircle to incircle is:
(a) 3 : 1
(b) 4 : 1
(c) 9 : 1
(d) 16 : 1
13. If the difference between the areas of the circumcircle and the incircle of an equilateral triangle is 88 cm², then the area of the triangle is (Take π = 22/7):
(a) 36√3 cm²
(b) 48√3 cm²
(c) 64√3 cm²
(d) 72√3 cm²
14. A circle is inscribed in an equilateral triangle. Another equilateral triangle is inscribed in the same circle. If the side of the larger equilateral triangle is 12 cm, then the ratio of the areas of the larger triangle to the smaller triangle is:
(a) 3 : 1
(b) 4 : 1
(c) 9 : 1
(d) 12 : 1
15. The ratio of the areas of the circumcircle and the incircle of an equilateral triangle is:
(a) 2 : 1
(b) 3 : 1
(c) 4 : 1
(d) 9 : 1
16. An equilateral triangle is drawn on the side of a square. The ratio of the area of the triangle to the area of the square is:
(a) 3 : 4
(b) 4 : 3
(c) 1 : 2
(d) 2 : 1
17. The median of an equilateral triangle is 12 cm. The area (in cm²) of the triangle is:
(a) 48√3
(b) 72√3
(c) 96√3
(d) 144√3
18. If the side of an equilateral triangle is increased by 2 m, its area is increased by 12√3 sq. metres. The original length of each side of the triangle is:
(a) 4 m
(b) 6 m
(c) 8 m
(d) 10 m
19. If the altitude of an equilateral triangle is 9√3 cm, then the area of the triangle is:
(a) 108 cm²
(b) 81 cm²
(c) 72 cm²
(d) 54 cm²
20. The area of an equilateral triangle inscribed in a circle is 12√3 cm². The area of the circle is:
(a) 48 cm²
(b) 36 cm²
(c) 64 cm²
(d) 72 cm²
21. A circle is inscribed in an equilateral triangle of side 12 cm. The area of the portion between the triangle and the circle is:
(a) 36 cm²
(b) 24 cm²
(c) 48 cm²
(d) 30 cm²
1. The area of an equilateral triangle is 144√3 sq. m. Its perimeter is:
(a) 36 m
(b) 48 m
(c) 60 m
(d) 72 m
2. From a point in the interior of an equilateral triangle, the perpendicular distances to the three sides are 2 cm, 4 cm and 6 cm. The perimeter (in cm) of the triangle is:
(a) 18
(b) 24
(c) 36
(d) 42
3. If the length of each median of an equilateral triangle is 8√3 cm, then the perimeter of the triangle is:
(a) 24 cm
(b) 36 cm
(c) 48 cm
(d) 60 cm
4. The area of the circumcircle of an equilateral triangle is 12π sq. cm. The perimeter of the triangle is:
(a) 18 cm
(b) 24 cm
(c) 36 cm
(d) 48 cm
5. The sides of an equilateral triangle are increased by 10%, 20%, and 30% respectively to form a new triangle. The increase in the perimeter of the equilateral triangle is:
(a) 25%
(b) 20%
(c) 30%
(d) 35%
6. If the perimeter of an equilateral triangle is 24 cm, then the length of each median of the triangle is:
(a) 4√3 cm
(b) 6√3 cm
(c) 8√3 cm
(d) 12√3 cm
7. The inradius of an equilateral triangle is 2 cm. The perimeter of the triangle is:
(a) 18 cm
(b) 24 cm
(c) 12 cm
(d) 30 cm
8. The radius of the incircle of an equilateral triangle of side 6 units is x cm. The value of x is:
(a) 1
(b) 2
(c) 3
(d) 4
9. The length of a side of an equilateral triangle is 14 cm. Find the area of the region lying between the circumcircle and the incircle of the triangle. (Take π = 22/7)
(a) 132 cm²
(b) 154 cm²
(c) 176 cm²
(d) 196 cm²