(1 mark each)
answers for each of the following questions :
(1) If the length of diagonals of rhombus are 12.2 cm and 8.5 cm. then its area is
(A) 1037 sq cm (B) 1073 sq cm U) 51.85 sq cm (D) 51.58 sq cm
(2) If the area of a parallelogram is 150 sq cm and its base is 10 cm, then the height of parallelogram is
(A) 10 cm s 15 cm
(C) 7.5 cm (D) 5 cm
(3) If the radius of the circle is 28 cm, then the area of the circle is
(AX 2464 sq cm (B) 2446 sq cm (C) 176 sq cm (D) 167 sq cm
(4) 1 acre is nearly
(A) 0.5 hectare 4B) 0.4 hectare
(C) 0.2 hectare
(D) 1 hectare
(5) If a trapezium of height 10 cm has area equal to the rhombus whose diagonals are of length 20 cm and 25 cm. then
sum of parallel sides of trapezium is
(A) 25 cm (B) 20 cm (C) 100 cm (D) 50 cm
Answers
Answer:
1. (C) 51.85 sq cm
2. (B) 15 cm
3. (A) 2464 sq cm
4. (B) 0.4 hectare
5. (D) 50 cm
Explanation:
1.
First diagonal = 12.2 cm = p
Second diagonal = 8.5 cm = q
Area of rhombus
= pq / 2
= 12.2 × 8.5 / 2
= 103.7 / 2
= 51.85 sq cm.
Hence, area of rhombus is 51.85 sq cm.
2.
Area = 150 sq cm = a
Base = 10 cm = b
Height
= a / b
= 150 / 10
= 15 cm
Hence, height of parallels is 15 cm.
3.
Radius = 28 cm = r
Area
= π × r × r
= 22/7 × 28 × 28
= 22/7 × 784
= 2464 sq cm
Hence, area if the circle is 2464 sq cm.
4.
1 acre = 0.405 hectare
So, approx = 0.4 hectare
Hence, 1 acre = 0.4 hectare (approx).
5.
First diagonal = 20 cm = p
Second diagonal = 25 cm = q
Area of Rhombus
= pq / 2
= 20 × 25 / 2
= 500 / 2
= 250 sq cm
Area of Trapezium
= Area of Rhombus
= 250 sq cm
We know that
Area of Trapezium = a + b / 2 × h
250 sq cm = a + b / 2 × 10cm
250 × 2 = a + b × 10
500 = a + b × 10
500 ÷ 10 = a + b
50 cm = a + b
Hence, sum of parallel sides of trapezium is 50 cm.