Questions: Area

Area24 min readLesson 6 of 6

in hinglish

Is page ke liye Hinglish recap pehle. Area unit squares ki ginti hai, isliye rectangle ka area length \times width aur square ka side \times side hota hai. Rectangle ka diagonal use do congruent triangles mein todta hai, isliye triangle ka area ½ \times base \times height hota hai; height base ke perpendicular honi chahiye. Parallelogram = base \times height, rhombus = ½ \times diagonals ka product, aur trapezium = ½ \times height \times (parallel sides ka sum). Perimeter area nahi hota: same perimeter wale regions ka area alag ho sakta hai. Composite shapes ko rectangles ya triangles mein tod kar areas jodo ya subtract karo. Unit conversions mein 1 in² = 6.4516 cm² aur 1 acre = 43,560 ft²; side double hone par area 4 guna hota hai. Har jawab ko units ke saath likho aur figure ki labelling se verify karo.

Q1 Find the area and perimeter of a 9 cm by 6 cm rectangle. Answer (English): Area = 9 \times 6 = 54 cm². Perimeter = 2 \times (9 + 6) = 30 cm. The area counts unit squares inside; the perimeter is the boundary length. They are different measures and cannot be swapped. Hinglish: Area = 9 \times 6 = 54 cm² aur perimeter = 2 \times (9 + 6) = 30 cm. Area andar ke unit squares ginti hai aur perimeter boundary ki lambai hai; dono alag measures hain.

Q2 Find the area of a triangle with base 14 cm and height 9 cm. Answer (English): Area = ½ \times 14 \times 9 = 63 cm². The height must be the perpendicular distance from the opposite vertex to the line containing the base, not the length of a slanted side. Hinglish: Area = ½ \times 14 \times 9 = 63 cm². Height base wali line tak perpendicular distance hoti hai, koi slanted side nahi.

Q3 A parallelogram has base 7 cm and height 4.5 cm. Find its area. Answer (English): Area = base \times height = 7 \times 4.5 = 31.5 cm². Pair the base with its own perpendicular height; a slanted side is longer and cannot be used as the height. Hinglish: Area = base \times height = 7 \times 4.5 = 31.5 cm². Base ke saath usi ka perpendicular height use karo; slanted side height nahi hoti.

Q4 A rhombus has diagonals 16 cm and 9 cm. Work out its area. Answer (English): Area = ½ \times 16 \times 9 = 72 cm². The diagonals of a rhombus are perpendicular, and the rhombus is made of four right triangles whose areas add to this value. Hinglish: Area = ½ \times 16 \times 9 = 72 cm². Rhombus ke diagonals perpendicular hote hain, aur char right triangles mil kar yeh area dete hain.

Q5 Find the area of a trapezium with parallel sides 8 cm and 14 cm and height 5 cm. Answer (English): Area = ½ \times height \times (sum of parallel sides) = ½ \times 5 \times (8 + 14) = ½ \times 5 \times 22 = 55 cm². The formula is the average of the parallel sides multiplied by the height. Hinglish: Area = ½ \times height \times (parallel sides ka sum) = ½ \times 5 \times (8 + 14) = 55 cm². Yeh formula parallel sides ke average ko height se multiply karta hai.

Q6 A triangle has area 36 cm² and height 8 cm. Find its base. Answer (English): Use ½ \times base \times height = 36, so ½ \times base \times 8 = 36, 4 \times base = 36 and base = 9 cm. Substituting back gives ½ \times 9 \times 8 = 36 cm². Hinglish: ½ \times base \times height = 36, isliye ½ \times base \times 8 = 36, 4 \times base = 36 aur base = 9 cm. Check: ½ \times 9 \times 8 = 36 cm².

Q7 A square has side 10 cm. Its side is doubled. What happens to its area? Answer (English): The original area is 100 cm². The new side is 20 cm and the new area is 400 cm². The area becomes 4 times larger, because both the length and the width doubled; the increase is 300 cm². Hinglish: Pehla area 100 cm², naya side 20 cm aur naya area 400 cm². Area 4 guna ho jata hai kyunki length aur width dono double hue; increase 300 cm² hai.

Q8 A parallelogram and a rectangle have sides 6 cm and 5 cm. Which has the greater area, and why? Answer (English): The rectangle has area 30 cm². The parallelogram's height to the 6 cm base is less than 5 cm because its 5 cm side is slanted, so its area is less than 30 cm². The rectangle has the greater area, unless the parallelogram is itself a rectangle. Hinglish: Rectangle ka area 30 cm² hai. Parallelogram ka 6 cm base tak height 5 cm se kam hai kyunki 5 cm side slanted hai, isliye area 30 cm² se kam hai. Rectangle ka area zyada hai, jab tak parallelogram khud rectangle na ho.

Q9 A rectangular park is 20 m by 15 m. A path 2 m wide runs inside along its boundary. Find the area of the path. Answer (English): The park area is 300 m². The inner rectangle is (20 - 4) m by (15 - 4) m = 16 m by 11 m, with area 176 m². The path area is 300 - 176 = 124 m². Hinglish: Park ka area 300 m². Andar ka rectangle (20 - 4) \times (15 - 4) = 16 \times 11 = 176 m². Path ka area = 300 - 176 = 124 m².

Q10 Convert 4 square inches to square centimetres, using 1 inch = 2.54 cm. Answer (English): One square inch is 2.54 \times 2.54 = 6.4516 cm². Four square inches are 4 \times 6.4516 = 25.8064 cm². The length conversion is squared because area has two dimensions. Hinglish: Ek square inch = 2.54 \times 2.54 = 6.4516 cm². Char square inches = 4 \times 6.4516 = 25.8064 cm². Area mein do dimensions hote hain, isliye length conversion ka square lagta hai.

Quiz pointer The five-question quiz for this chapter is separate from these answers. Take it without looking back, then redo any question you missed by writing the formula first. Check the units on every line, and remember that the height in a triangle or parallelogram must be perpendicular to the chosen base.