Area of a Rhombus | Mensuration | Assessment | English | Grade 8

If d₁ and d₂ are the diagonals of a rhombus, then its area is equal to ____________.

• (d₁ + d₂)/2

• (d₁ - d₂)/2

• (d₁ × d₂)/2

• (d₁ + d₂) × 2

If the diagonals of a rhombus are of lengths 15 cm and 21 cm then its area is equal to _________.

• 156.5 cm²

• 157.5 cm²

• 158.5 cm²

• 159.5 cm²

Answer explanation

Area of rhombus = (d₁ × d₂)/2 = (15 × 21)/2 = 157.5 cm² So, Option 2 is correct.

If the diagonals of a rhombus are of lengths 74 cm and 480 mm then its area is equal to _________.

• 1776 cm²

• 1778 cm²

• 1775 cm²

• 1772 cm²

Answer explanation

480 mm = 48 cm (10 mm = 1 cm) Area of rhombus = Product of diagonals/2 = (74 × 48)/2 = 1776 cm² So, Option 1 is correct.

If the area of a rhombus is 320 cm² and the length one of its diagonal is 40 cm, what is the length of the other diagonal?

• 18 cm

• 16 cm

• 12 cm

• 15 cm

Answer explanation

Let the length of the two diagonals be denoted by d₁ and d₂, respectively. Area = 320 cm², d₁ = 40 cm and d₂ is unknown Area of rhombus = (d₁ × d₂)/2 According to the question, we have, 320 = (40 × d₂)/2 320 = 20 × d₂ d₂ = 320/20 = 16 cm So, Option 2 is correct.

Manish makes 20 identical pieces of 'Kaju Katli' whose diagonals are 2 cm and 3.5 cm respectively. He wants to put edible silver sheet on the top surface of all the pieces which costs ₹ 40 per sq. cm. What will be the cost of the silver sheet required by Manish?

• ₹ 2700

• ₹ 2500

• ₹ 2800

• ₹ 2300

Answer explanation

As shown in the figure, the top surface of 'Kaju Katli' is in the shape of rhombus. Area of rhombus = Product of diagonals/2 Area of top surface of one kaju katli piece = (2 × 3.5)/2 = 3.5 cm Total area for 20 pieces= 20 × 3.5 cm² = 70 cm² Cost of silver sheet per cm² = ₹ 40 Total cost of silver sheet = 70 × ₹ 40 = ₹ 2800 So, Option 3 is correct.

Rakesh's father wants to divide his land equally among his four children. If his land is in the shape of a rhombus whose two diagonals are of lengths 88 m and 52 m respectively, then how much land will be given to Rakesh?

• 575 m²

• 572 m²

• 578 m²

• 576 m²

Answer explanation

The land is in the shape of a rhombus. Area of rhombus = Product of diagonals/2 Area of the land = (88 × 52)/2 = 2288 m² Part of the land to be given to Rakesh = 2288/4 = 572 m² So, Option 2 is correct.

If the perimeter of a rhombus is 80 cm and the length of one of its diagonals is 24 cm, what is the area of the rhombus?

• 382 cm²

• 96 cm²

• 192 cm²

• 384 cm²

Answer explanation

Perimeter of rhombus = 80 cm Side of rhombus = 80/4 = 20 cm Length of one diagonal = 24 cm Consider a right triangle, triangle AOD, AO = ?, OD = 24/2 = 12 cm, AD = 20 cm By Pythagoras theorem, AO² = AD² - OD² = (20² - 12² ) = (400 - 144) = 256 So, AO = √256 = 16 cm Half of another diagonal of rhombus = AO = 16 cm Length of the other diagonal of rhombus = AC = 2 × 16 = 32 cm Hence area of rhombus = Product of diagonals/2 = (24 × 32)/2 = 384 cm² So, Option 4 is correct.