1. Draw a rectangle with a length of 7 cm and a width of 4 cm; now draw a square with the same area as that rectangle. (Only the construction marks are required.)
2. Draw a square having the same area as a rectangle of length 10 cm and width 5 cm. (Only construction marks are required.)
3. Draw a triangle in which two sides are 9 cm and 7 cm, and the included angle between them is 60°. Then draw the incircle of that triangle. (Only construction marks are required.)
4. Draw a triangle ABC such that BC = 6 cm, CA = 5.5 cm, and AB = 4.5 cm. Then draw the incircle of ∆ABC. (Only construction marks are required.)
5. Draw triangle ABC such that BC = 7 cm, AB = 5 cm, and AC = 6 cm. Then draw the circumcircle of triangle ABC. (Only construction marks are required.)
6. Draw a right-angled triangle whose two sides adjacent to the right angle are 4.5 cm and 6 cm. Then draw the incircle of that triangle. (Only construction marks are required.)
7. Draw a square with the same area as a rectangle whose side lengths are 8 cm and 6 cm.
8. Draw a right-angled triangle in which the two sides adjacent to the right angle are 5 cm and 6 cm. Then draw a square that has the same area as that triangle.
9. Draw a right-angled triangle whose two sides adjacent to the right angle are 7 cm and 9 cm respectively. Then draw the incircle of that triangle. (Only construction marks are required.)
10. Draw a right-angled triangle whose hypotenuse is 10 cm and one of the other sides is 6.5 cm. Then, draw the incircle of this triangle. (Only construction marks are required.)
11. Draw a triangle with side lengths of 5 cm, 6 cm, and 7 cm. Then, draw the incircle of that triangle (only construction marks should be included).
12. Draw triangle ABC where AB = 8 cm, BC = 6 cm, and ∠ABC = 60°. Construct the circumcircle of that triangle. (Only construction marks are required).
13. Draw a square with the same area as a rectangle whose side lengths are 6 cm and 4 cm.
14. Draw a square with the same area as an isosceles triangle whose base length is 7 cm and each of the equal sides is 5 cm.
15. - sin 280 sec 210 - 1 The dimensions of a cuboid are 12 cm, 6 cm, and 3 cm. What will be the length of each edge of a cube having the same volume as that cuboid?
16. Draw a triangle with sides of 6 cm, 8 cm, and 10 cm. Then draw the incircle of that triangle.
17. If a triangle similar to one with sides 4 cm, 6 cm, and 8 cm has its largest side measuring 6 cm, what is the length of the smallest side of that triangle?
(a) 4 cm (b) 3 cm (c) 2 cm (d) 5 cm
18. Draw an equilateral triangle with side length 6 cm and then draw its incircle. (Only construction marks are required.)
19. If the diagonal of a rectangle is 10 cm and its area is 62.5 square cm, then the sum of the length and breadth of the rectangle is —
(a) 12 cm (b) 15 cm (c) 20 cm (d) 25 cm
20. Draw a right-angled triangle whose hypotenuse is 9 cm and one of the other sides is 5.5 cm. Then draw an incircle of the triangle. (Only the construction marks are required.)
21. Draw a right-angled triangle whose two sides adjacent to the right angle are 8 cm and 6 cm respectively, and draw an incircle of the triangle. (Only construction marks are required)
22. If two solid spheres with diameters of 1 cm and 6 cm are melted and recast into a hollow sphere with a thickness of 1 cm, then what is the outer surface area of the new hollow sphere?
23. A brass plate has a square base with side length \(x\) cm, thickness 1 mm, and a total weight of 4725 grams. If the weight of 1 cubic centimeter of brass is 8.4 grams, then calculate and write the value of \(x\).
24. Draw a triangle with two sides measuring 7.6 cm and 6 cm, and an included angle of 75\(^o\). Then, construct its incircle.
25. Draw a triangle with three sides measuring 7 cm, 6 cm, and 5.5 cm. Then, draw an incircle for that triangle.
26. Draw a triangle with a base length of 6.2 cm and the two adjacent angles measuring 50° and 75°; then construct its incircle. (Only provide the construction marks.)
27. Draw a triangle with two sides measuring 6.5 cm and 5.7 cm, and the included angle. Then, draw the incircle of the triangle.
28. Draw an isosceles triangle where the base length is 5 cm and each of the equal sides is 6 cm. Then, draw the incircle of the triangle. (Only construction marks should be indicated in each case.)
29. Draw a right-angled triangle with the two sides adjacent to the right angle measuring 4 cm each. Then draw the circumcircle of the triangle. (Only construction marks are required.)
30. A drum with a lid is made of thin steel sheet and has a diameter of 28 cm. If 2816 square cm of sheet metal is required to make the drum, then calculate and write the height of the drum.
