AREA OF QUADRILATERALS
Q1–10 of 70The area of a rectangular field is 2100 sq. metres. If the field is 60 metres long, what is its perimeter?
Calculate breadth as Area ÷ Length = 2100 ÷ 60 = 35 m. Then, find the perimeter using 2(Length + Breadth) = 2(60 + 35) = 240 m.
The length of a rectangle is 18 cm and its breadth is 10 cm. When the length is increased to 25 cm, what will be the breadth of the rectangle if the area remains the same?
The initial area is 18 × 10 = 180 cm². Since the area remains unchanged, the new breadth is Area ÷ New Length = 180 ÷ 25 = 7.2 cm.
A rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing. If the poles of the fence are kept 5 metres apart, how many poles will be needed?
The perimeter of the plot is 2(90 + 50) = 280 metres. For a closed loop, the number of poles needed is Perimeter ÷ Spacing = 280 ÷ 5 = 56 poles.
The length of a rectangular plot is 60% more than its breadth. If the difference between the length and the breadth of that rectangle is 24 cm, what is the area of that rectangle?
Let breadth be b; length l = 1.6b. Given l - b = 0.6b = 24 cm ⇒ b = 40 cm and l = 64 cm. Thus, Area = l × b = 64 × 40 = 2560 sq. cm.
A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, then what is the area of the parking space in square feet?
Let the unpainted side be a length L = 9 ft. The painted sides consist of two breadths and one length: 2B + 9 = 37 ⇒ B = 14 ft. Thus, Area = L × B = 9 × 14 = 126 sq. ft.
A man is walking in a rectangular field whose perimeter is 6 km. If the area of the rectangular field be 2 sq. km, then what is the difference between the length and breadth of the rectangle?
From perimeter 2(l + b) = 6 ⇒ l + b = 3 km, and area lb = 2 sq. km. Using (l - b)² = (l + b)² - 4lb = 3² - 4(2) = 1 ⇒ l - b = 1 km. |
A carpenter is designing a table. The table will be in the form of a rectangle whose length is 4 feet more than its width. How long should the table be if the carpenter wants the area of the table to be 45 sq ft?
Let width be w, so length l = w + 4. Area is w(w + 4) = 45. Solving w² + 4w - 45 = 0 yields w = 5 ft, so l = 5 + 4 = 9 ft.
The perimeter of a rectangular field is 480 metres and the ratio between the length and the breadth is 5 : 3. The area is
Perimeter 2(5x + 3x) = 480 ⇒ 16x = 480 ⇒ x = 30 m. Length is 150 m, breadth is 90 m, so Area = 150 × 90 = 13500 sq. m.
A rectangular farm has to be fenced on one long side, one short side and the diagonal. If the cost of fencing is ₹100 per m, the area of the farm is 1200 m² and the short side is 30 m long, how much would the job cost?
Short side B = 30 m, so long side L = 1200 ÷ 30 = 40 m. Diagonal D = √(40² + 30²) = 50 m. Total fenced length = 40 + 30 + 50 = 120 m. Cost = 120 × 100 = ₹12000.
The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is
Boundary perimeter = Speed × Time = 12000 × (8/60) = 1600 m. 2(3x + 2x) = 1600 ⇒ x = 160 m. Area = (3 × 160)(2 × 160) = 480 × 320 = 153600 sq. m.