The perimeter of a rhombus is 40 cm. If one diagonal is 16 cm, find : (i) its other diagonal (ii) its area

(i) Given: The perimeter of a rhombus = 40 cm. One diagonal = 16 cm. As we know, the perimeter of the rhombus = 4 x side ⇒ 4 x side = 40 cm ⇒ Side = cm ⇒ Side = 10 cm AB = 10 cm AC = 16 cm Then, OA = OC = = 8 cm Let OB be `a` cm. Since the diagonal of a rhombus bisect at 90°. Applying pythagoras theorem in triangle AOB, we get: AB 2 = OA 2 \+ OB 2 ⇒ (10) 2 = (8) 2 \+ a 2 ⇒ 100 = 64 \+ a 2 ⇒ a 2 = 100 \- 64 ⇒ a 2 = 36 ⇒ a = ⇒ a = 6 So, OB = 6 cm BD = 2 x 6 cm = 12 cm Hence, the length of other diagonal is 12 cm. (ii) As we know that area of rhombus = x product of its diagonal = x 16 x 12 cm 2 = x 192 cm 2 = 96 cm 2 Hence, the area of the rhombus is 96 cm 2 .

The adjacent sides of a parallelogram are 21 cm and 28 cm. If its one diagonal is 35 cm, find the area of the parallelogram.

View Answer Bookmark Now

The diagonals of a rhombus are 18 cm and 24 cm. Find :
(i) its area
(ii) length of its sides
(iii) its perimeter

View Answer Bookmark Now

The length of the diagonals of a rhombus is in the ratio 4 : 3. If its area is 384 cm², find its side.

View Answer Bookmark Now

A thin metal iron-sheet is a rhombus in shape, with each side 10 m. If one of its diagonals is 16 m, find the cost of painting its both sides at the rate of ₹ 6 per m².
Also, find the distance between the opposite sides of this rhombus.

View Answer Bookmark Now

Mathematics

The perimeter of a rhombus is 40 cm. If one diagonal is 16 cm, find :
(i) its other diagonal
(ii) its area

Area Trapezium Polygon

Related Questions

The adjacent sides of a parallelogram are 21 cm and 28 cm. If its one diagonal is 35 cm, find the area of the parallelogram.

The diagonals of a rhombus are 18 cm and 24 cm. Find :
(i) its area
(ii) length of its sides
(iii) its perimeter

The length of the diagonals of a rhombus is in the ratio 4 : 3. If its area is 384 cm², find its side.

A thin metal iron-sheet is a rhombus in shape, with each side 10 m. If one of its diagonals is 16 m, find the cost of painting its both sides at the rate of ₹ 6 per m².
Also, find the distance between the opposite sides of this rhombus.

Mathematics

The perimeter of a rhombus is 40 cm. If one diagonal is 16 cm, find :(i) its other diagonal(ii) its area

Area Trapezium Polygon

Related Questions

The adjacent sides of a parallelogram are 21 cm and 28 cm. If its one diagonal is 35 cm, find the area of the parallelogram.

The diagonals of a rhombus are 18 cm and 24 cm. Find :(i) its area(ii) length of its sides(iii) its perimeter

The length of the diagonals of a rhombus is in the ratio 4 : 3. If its area is 384 cm2, find its side.

A thin metal iron-sheet is a rhombus in shape, with each side 10 m. If one of its diagonals is 16 m, find the cost of painting its both sides at the rate of ₹ 6 per m2.Also, find the distance between the opposite sides of this rhombus.

The perimeter of a rhombus is 40 cm. If one diagonal is 16 cm, find :
(i) its other diagonal
(ii) its area

The diagonals of a rhombus are 18 cm and 24 cm. Find :
(i) its area
(ii) length of its sides
(iii) its perimeter

The length of the diagonals of a rhombus is in the ratio 4 : 3. If its area is 384 cm², find its side.

A thin metal iron-sheet is a rhombus in shape, with each side 10 m. If one of its diagonals is 16 m, find the cost of painting its both sides at the rate of ₹ 6 per m².
Also, find the distance between the opposite sides of this rhombus.