In the following figure, ABCD is a trapezium of area 24.5 cm² , If AD || BC, ∠DAB = 90°, AD = 10 cm, BC = 4 cm and ABE is quadrant of a circle, then find the area of the shaded region.
Answers
Answer:
The area of the shaded region = 14.875 cm².
Step-by-step explanation:
Given :
Area of trapezium ABCD, A = 24.5 cm²
AD || BC, ∠DAB = 90°, AD = 10 cm, BC = 4 cm and ABE is quadrant of a circle.
Area of the trapezium, A = ½ (sum of parallel sides) × perpendicualr distance between the parallel sides
A = ½ (AD + BC) × AB
24.5 = ½ (10 + 4) × AB
24.5 × 2 = 14 AB
49 = 14 AB
AB = 49/14
AB = 7/2
AB = 3.5 cm
Radius of the quadrant of the circle ,r = AB = 3.5 cm
Area of the quadrant of the circle = ¼ ×πr²
= (1/4) (22/7 x 3.5 x 3.5)
= 9.625 cm²
Area of the quadrant of the circle,ABE = 9.625 cm²
Area of the shaded region = Area of the trapezium,ABCD - Area of the quadrant of the circle,ABE
= 24.5 - 9.625
Area of the shaded region = 14.875 cm²
Hence, the area of the shaded region = 14.875 cm².
HOPE THIS ANSWER WILL HELP YOU….
It is given that the area of trapezium ABCD is 24.5 cm^2 .
And AD || BC
<DAB = 90°
AD = 10 cm
BC = 4cm
As we know that
area of trapezium = 1/2 + (sum of parallel sides )× height
=> 24.5 = 1/2 ( AD + BC )× AB
=> 24.5 × 2 = (10+4) × AB
=> 49 = 14 × AB
=> AB = 49/14
=> AB = 3.5 cm
Now,
Area of quadrant
Area of quadrant = 9.625 cm^2 .
Now ,
Area of shaded region = area of trapezium - area of quadrant
Hence , the area of shaded region is 14.875 cm^2 .