Question 1: Find the area of the parallelogram whose:
(i) base and height
(ii) base and height
Answer:
(i)
(ii)
Question 2: The height of a parallelogram is one-third of its base. If the area of the parallelogram is , find the height and the base.
Answer:
, Base
Therefore Height , Base
Question 3: is a parallelogram with
and
. If the distance between. its larger sides is
, find
(i) the area of the parallelogram;
(ii) the distance between its shorter sides
Answer:
(i)
(ii) Let the distance between the shorter sides
Question 4: is a parallelogram having adjacent sides
and
. If its area is
, find the distance between its longer sides and that between its shorter sides.
Answer:
Let the distance between the longer sides
Let the distance between the shorter sides
Question 5: In the adjoining figure, is a parallelogram in which
and diagonal
. Find
(i) the area of parallelogram
;
(ii) the distance between and
;
(iii) the distance between and
.
Answer:
(i)
Therefore Area of parallelogram
(ii) Let the distance between the longer sides
(iii) Let the distance between the shorter sides
Question 6: Find the area of a rhombus whose perimeter is and altitude is
.
Answer:
Note: Rhombus is a special parallelogram where all sides are equal.
Question 7: The area of a rhombus is and its altitude is
. Find the perimeter of the rhombus.
Answer:
Question 8: The area of a rhombus is and its perimeter is
. Find its altitude.
Answer:
Area of a Rhombus:
Question 9: Find the area of rhombus whose diagonals are : (i) (ii)
Answer:
(i)
(ii)
Question 10: The area of a rhombus is . If one of the diagonals is
long, find the length of the other diagonal.
Answer:
Diagonal
Question 11: Find the area of a rhombus, each side of which measures and one of whose diagonals is
.
Answer:
Therefore Area of parallelogram
Question 12: Find the area of a trapezium whose parallel sides are and
and the distance between them is
.
Answer:
Question 13: Find the area of a trapezium whose parallel sides are and
and the distance between them is
.
Answer:
Question 14: The lengths of parallel sides of a trapezium are in the ratio and the distance between them is
. If the area of the trapezium is
, find the Lengths of its parallel sides.
Answer:
Let the length of the parallel sides be and
respectively.
Therefore
Hence the length of the parallel sides be and
respectively.
Question 15: The height of the trapezium of the area is
. If one of the base is
, find the other.
Answer:
Let the other base be
Question 16: In the adjoining figure, is a trapezium in which parallel sides are
and the non-parallel sides are
and
. Find the area of the trapezium.
Answer:
Let and let the distance between the parallel lines
Question 17: The parallel sides of a trapezium are and
. Its non-parallel sides are both equal, each being
. Find the area of the trapezium.
Answer:
Let and let the distance between the parallel lines
Question 18: The area of a trapezium is and its height is
. If one of the parallel sides is longer than the other by
, find the two parallel sides.
Answer:
Let the length of the parallel sides be and
respectively.
Therefore
Hence the length of the parallel sides be and
respectively.
Question 19: In the adjoining figure, is a rectangle in which
and
. Find the area of the shaded region
.
Answer:
Question 20: Find the area of the figure , given alongside, it being given that
Answer:
Area of
Therefore total area
Question 21: Find the area of the shaded region in the figure given alongside.
Answer:
Area of top rectangle
Area of bottom rectangle
Therefore total area
Question 22: Find the area of the shaded region given below:
Answer:
Area of the shaded region
Question 23: Find the area of the figure , it being given that:
,
.
Answer:
Area of the shaded region
Question 24: Find the area of the field
, in which
and
,
and
Answer:
Area of
Area of
Area of
Area of
Area of
Area of
Total area