Question

Find the area of a rhombus whose side is 7.5cm altitude is 4cm and diagonal is 8 cm find other diagonal

Answer 1

Answer:

Step-by-step explanation:

Area of rhombus is = Base X Height

Base= 7.5cm, height= 4cm

Area= 30cm sq.

Area of rhombus has another formula

1/2* D1*D2

1/2*8*D2=30

4*D2=30

D2= 30/4= 7.5 cm

Ans is 7.5cm

Answer 2

Given:

• Side of the rhombus = 7.5 cm
• The Altitude of the rhombus = 4 cm
• The diagonal of the rhombus = 8cm

To Find:

• The area of the rhombus and the other diagonal.

Solution:

We already know that a rhombus is the same as a parallelogram, therefore we get,

Area of a rhombus = Area of a parallelogram = Base×Height

∴ Area of a rhombus = Base of the rhombus × height/altitude of the rhombus,

⇒ Area of a rhombus = 7.5×4,

Multiplying base and height by substituting the given values in the above equation we get,

⇒ Area of rhombus = 30 $cm^2$

To find the second diagonal of the rhombus we use one more formula  which is given by,

⇒Area of a rhombus = $\frac{1}{2}*d_1*d_2$  

Where $d_1$ and $d_2$ are the two diagonals.

⇒30 = $\frac{1}{2}*8*d_2$

In the above equation, we substituted the value of one diagonal from the given data and the area which we calculated previously to find the value of the second diagonal.

⇒$d_2$ = $\frac{30*2}{8}$ = 7.5 cm

⇒$d_2$ = 7.5 cm

∴ The area of a rhombus = 30 $cm^2$ and the second diagonal, $d_2$ = 7.5 cm