Question

Solve the sums.

5. The area of rhombus is 120 cm 2

and one of the diagonals is 8 cm. Find the other

diagonal.


6. The diagonal of a quadrilateral shaped field is 24 m and the remaining opposite

vertical are 8 m and 13 m. Find the area of the field.​

Answer 1

Answer:

5. 30 cm

6. 252 m²

Answer 2

Question 1 :

The area of rhombus is 120 cm² and one of the diagonals is 8 cm. Find the other diagonal.

★Given :

• Area of rhombus = 120 cm²
• First Diagonal = 8 cm

★To find :

• The other diagonal

★Solution :

Let's consider the second or other diagonal of the rhombus be x.

Finding the second diagonal by applying :

$\star{\text{\sf{\red{Area of Rhombus :}}}}$

${\red{\sf{\dfrac{Diagonal_1 \times{Diagonal_2}}{2}}}}$

Putting the value :

$\mapsto\sf{120=}\dfrac{8 \times{x}}{2}$

$\mapsto\sf{120\times2=8x}$

$\mapsto\sf{240=8x}$

$\mapsto\sf{x=}\dfrac{\cancel{240}^{30}}{\cancel{8}^1}$

$\mapsto\sf{x=30cm}$

Thus,the other diagonal of the rhombus is 30cm.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Question 2 :

The diagonal of a quadrilateral shaped field is 24 m and the remaining opposite vertical are 8 m and 13 m. Find the area of the field.

★Given :

• Diagonal of a quadrilateral = 24 m
• The opposite vertices are = 8m & 13 m

★To find :

• The area of the field(quadrilateral field)

★Solution :

To find the area of the Quadrilateral we apply the formula :

$\star{\text{\sf{\blue{Area of quadrilateral : }}}}$

${\tiny{\sf{\blue{\dfrac{1}{2}}}}}{\text{\sf{\blue{(Diagonal)(Sum of perpendicular diagonals)}}}}$

Putting the values :

$\leadsto\sf{Area=}\dfrac{1}{2}{\times24\times(8+13)}$

$\leadsto\sf{Area=}\dfrac{1}{\cancel{2}^2}{\times\cancel{24}^{12}\times(8+13)}$

$\leadsto\sf{Area=12\times(8+13)}$

$\leadsto\sf{Area=12\times21}$

$\leadsto\sf{Area=252m^2}$

Hence,the area of the Quadrilateral shaped Field is 252 m²

▬▬▬▬▬▬▬▬▬▬