AP Board 7th Class Maths Solutions Chapter 13 Area and Perimeter Ex 4

AP State Syllabus AP Board 7th Class Maths Solutions Chapter 13 Area and Perimeter Ex 4 Textbook Questions and Answers.

AP State Syllabus 7th Class Maths Solutions 13th Lesson Area and Perimeter Exercise 4

Question 1.
Find the area of the following rhombuses.

Solution:
Area = \(\frac { 1 }{ 2 }\)d₁d₂
d₁ = 5 + 5 = 10cm
d₂ = 2 + 2 = 4cm
A = \(\frac { 1 }{ 2 }\) × 10 × 4 = 20 cm²

d₁ = 3 + 3 = 6 cm
d₂ = 4 + 4 = 8cm
Area = \(\frac { 1 }{ 2 }\)d₁d₂
= \(\frac { 1 }{ 2 }\) × 6 × 8
= 24 cm²

Question 2.
Find the missing values.

Diagonal – 1 (d1)	Diagonal – 2 (d2)	Area of the rhombus
12cm	16cm
27mm		2025mm2
14m	57.6m

Solution:

Diagonal – 1 (d1)	Diagonal – 2 (d2)	Area of the rhombus
12cm	16cm	\(\frac{1}{2}\) × 12 × 16 = 96cm2
27mm	\(\frac{2025 \times 2}{27}\) = 150mm	2025mm2
14m	57.6m	\(\frac{1}{2}\) × 24 × 57.6 = 691.2 m2

Question 3.
If length of diagonal of a rhombus whose area 216 sq. cm. is 24 cm. when find the length of second diagonal.
Solution:
Given: Length of one diagonal d₁ = 24cm, d₂ =?
Area = \(\frac { 1 }{ 2 }\)d₁d₂ = 216
\(\frac { 1 }{ 2 }\) × d₁ × d₂ = 216
\(\frac { 1 }{ 2 }\) × 24 × d₂ = 216
d₂ = \(\frac{216}{12}\) = 18

Question 4.
The floor of a building consists of3 000 tiles which are rhombus shaped. The diagonals of each of the tiles are 45 cm and 30 cm. Find the total cost of polishing the floor, if cost per m² is Rs.2.50.
Solution:
Diagonals of each (shape / rhombus) tiles
d₁ = 45cm, d₂ = 30cm
Total tiles = 3000
Total area = 3000 × Area of each tile = 3000 × \(\frac { 1 }{ 2 }\) × d₁ × d₂
= 3000 x \(\frac { 1 }{ 2 }\) × 45 × 30 = 2025000 cm²
= \(\frac{2025000}{100 \times 100}\) m² = 202.5m²
∴ Cost of polishing the floor at the rate of Rs. 2.50 per a square metre 202.5 × 2.50 = Rs. 506.25