[Exercise- Page 90]
E.5.1. To measure the area of the shape in the given figure- A, how will you use the properties of a right-angled triangle? Solve the problem and write the logic behind your solution.
If AD = 12 cm, find the length of BC.
Solution:
E.5.2. Prove that the diagonals of a square are equal. You may draw a figure or prove by cutting papers.
Solution:
E.5.3. Suppose length of four sides are 4 cm, 3 cm, 3.5 cm, 5 cm and one of the angles is 60 degrees. Construct the quadrilateral.
Solution:
E.5.4. In figure- B, AB = ?
Solution:
E.5.5. To color a wall of your school, suppose the base of a ladder of 15 m is placed at 12 m distance from the wall then determine the height of the wall up to the tip of the ladder.
Solution:
E.5.6. Calculate the perimeter of the given rectangle. (Figure- D)
Solution:
E.5.7. Suppose for a rhombus ABCD, the diagonals AC = 30 cm and BD = 16 cm. Calculate the perimeter of the rhombus.
Solution:
E.5.8. Check the validity of the statement, If (3, 4 and 5) are Pythagorean triplets, then (3k, 4k and 5k) are also Pythagorean triplets, where k is any positive integer.
Solution:
E.5.9. Verify the following statement by constructing a triangle or cutting papers, “The line segment joining the midpoints of any two sides of a triangle is parallel to the third side and half in length.”
Solution:
E.5.10. Suppose for a parallelogram the length of two adjacent sides are 6cm and 5cm and the angle between these sides is 50°. Construct the parallelogram.
Solution:
E.5.11. Suppose the length of a side of a square is 5 cm. Construct the square.
Solution:
E.5.12. Suppose for a parallelogram shaped land the length of two adjacent sides are 4 m and 5 m and length of a diagonal is 7 m. Determine the area of the land.
Solution:
E.5.13. For a rectangular land ABCD, AB = 10 m and diagonal AC = 16 m. If the intersecting point of the diagonals is G, calculate the area of ΔAGB.
Solution:
E.5.14. Measure the area of following shapes
a)
Solution:
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