CLASS IX
AREA OF TRIANGLE
1. The perimeter of a right – angled triangle is 144 cm and its hypotenuse is 144 cm
and its hypotenuse measures 65 cm. Find the lengths of other two sides and
calculate its area. Verify the result by using Heron’s formula.
2. find the area of a triangle, the two sides of which are 18 cm and 10 cm and the
perimeter is 42 cm.
3. Find the area of ∆ ABC in which ∠ B = 900, ∠ C = 450 and AC = 6 cm.
4. Find the area of a right angled triangle, if the radius of its circumcirle is 5 cm and
the altitude drawn to the hypotenuse is 4 cm.
5. The sides of a triangle are 10 cm, 24 cm and 26 cm. Find its area and the longest
altitude.
6. One side of a right- triangle measures 126 cm and the difference in lengths of its
hypotenuse and other side is 42 cm. Find the measures of its two unknown sides
and calculate its area. Verify the result by using Heron’s formula.
7. A triangular park in a city has dimensions 30 m x 26 m x 28 m. A gardener has to
plant grass inside the park at the rate of Rs 1.50 per sq m. Find the amount to be
paid to the gardener.
8. Find the area of a triangle with perimeter 22 cm. One side 9 cm and difference of
other two sides is 7 cm.
9. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its
base is 3: 2. Find the area of triangle.
10. Find the area of a parallelogram, whose one diagonal is 6.8 cm and the
perpendicular distance of this diagonal from an opposite vertex is 7.5 cm.
11. OABC is a rhombus, whose three vertices A, B and C lie on a circle with centre O.
If the radius of the circle is 10 cm. Find the area of the rhombus.
12. The perimeter of a rhombus is 146 cm. One of the diagonal is 55 cm. Find the
length of the other diagonal and the area of the rhombus.
13. The lengths of two adjacent sides of a parallelogram are respectively 51 cm and 37
cm. One of its diagonals is 20 cm. Find the area of the parallelogram.
14. A park, in the shape of a quadrilateral ABCD, has ∠ C = 900, AB = 9 m, BC = 12 m,
CD = 5 m and AD = 8 m. How much area does it occupy?
15. Find the area of quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 6 cm,
DA = 5 cm and diagonal AC = 5 cm.
16. Find the area of a quadrilateral ABCD whose sides are 9 m, 40 m, 28 m and 15 m
respectively and the angle between first two sides is right – angle.
17. A trapezium has parallel sides of lengths 18 cm and 10 cm. Find its area, if the
other two sides are each of length 5 cm.
18. A field is in the shape of a trapezium having parallel sides 90 m and 30 m. These
sides meet the third side at right angles. The length of the fourth side is 100 m. If it
costs Rs 4 to plough 1 sq m of the field, find the total cost of ploughing the field.
19. A trapezium has parallel sides of lengths 25 cm and 13 cm. Find its area, if the
other two sides are each of length 15 cm.
20. The sides of a quadrilateral field, taken in order are 26 m, 27 m, 7 m and 24 m
respectively and the angle contained by the last two sides is a right angle. Find its
area.
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