Question

Find the area of the rhombus if the length of
each side be 7cm and the corresponding altitude
be 8cm
by the formula 1/2product of its diagnols​

Answer 1

Answer:

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Step-by-step explanation:

Rhombus

Solve for area

a Side

7

cm

p Diagonal

Enter value

cm

Answer 2

Area of rhombus ABCD = 2 Area of ∆ ABC

= 2 × 1/2 AB × CD sq units.

= 2 × 1/2 b × h sq. units

= base x height sq. units

Also, area of rhombus = 4 × area of ∆ AOB

= 4 × 1/2 × AO × OB sq. units

= 4 × 1/2 × 1/2 d₂ × 1/2 d₁ sq. units

= 4 × 1/8 d₁ × d₂ square units

= 1/2 × d₁ × d₂; where d₁ and d₂ are diagonals.

Therefore, area of rhombus = 1/2 (product of diagonals) square units

• Perimeter of rhombus = 4 × side

Worked-out examples on area of rhombus:

Example :-

1. Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm.

Solution:

ABCD is a rhombus in which AB = BC = CD = DA = 17 cm

AC = 16 cm

how to find the area of rhombus,area of rhombus

Therefore, AO = 8 cm

In ∆ AOD,

AD² = AO² + OD²

⇒ 17² = 8² + OD²

⇒ 289 = 64 + OD²

⇒ 225 = OD²

⇒ OD = 15

Therefore, BD = 2 OD

= 2 × 15

= 30 cm

Now, area of rhombus

= 1/2 × d₁ × d₂

= 1/2 × 16 × 30

= 240 cm²

Example :-

2. Find the altitude of the rhombus whose area is 315 cm² and its perimeter is 180 cm.

Solution:

Since, the perimeter of rhombus = 180 cm

Therefore, side of rhombus = P/4 = 180/4 = 45 cm

Now, area of rhombus = b × h

⇒ 315 = 45 × h

⇒ h = 315/45

⇒ h =7 cm

Therefore, altitude of the rhombus is 7 cm.

Follow the examples and do yourself

Hope it's help u