Here we will be learning that How we are going to solve Area related Questions of various geometrical shapes and figures.
Geometry is concerned in calculating the length, perimeter, area and volume of various geometric figures and shapes
1: The sides of a triangle are in the ratio $\frac{1}{2}:\frac{1}{3}: \frac{1}{4}$. Find the smallest side of the triangle, if the perimeter of the triangle is $78$ cm.
Options:
A. 20 cm
B. 24 cm
C. 36 cm
D. 18 cm
Solution:
Perimeter of the triangle = 78 cm
Therefore 6x + 4x + 3x = 78
13x = 78
x = 6
The Sides are :
6 x 6 = 36 cm
6 x 4 = 24 cm
6 x 3 = 18 cm
Correct option: D
2. A rope makes 120 rounds of cylinder with base radius 10 cm. How many times it can go round a cylinder with base radius 20 cm?
Options:
A. 70 cm
B. 60 cm
C. 45 cm
D. 50 cm
Solution:
If radius is more, then rounds will be less as the length of the ropes remains the same
x = 2*π*10*120…(1)
Similarly,
x = 2 * π * 20 * a…(2)
From (1) and (2)
10 * 120 = 20 * a
=> a = 60
Correct option: B
3. Find the area of a parallelogram with base 16 cm and height 7 cm.
Options:
A. 112 cm²
B. 128 cm²
C. 102 cm²
D. 212 cm²
Solution:
Area of parallelogram = b * h
Area of parallelogram = 16 * 7 = 112 cm²
Correct option: A
1: A rectangular piece of cloth when soaked in water, was found to have lost 20% of its length and 10% of its breadth. Calculate the total percentage of decrease in the area of rectangular piece of cloth?
Options:
A. 75% decrease
B. 28% increase
C. 28% decrease
D. 20% decrease
Solution:
Let the original length = l
Let the original breadth = b
Original Area = l * b
New length = $\frac{80}{100}$
New breadth = $\frac{90}{100}$
Decrease in the area = lb – $\frac{80}{100}$ x $\frac{90}{100}$
6 x 4 = 24 cm
6 x 3 = 18 cm
Correct option: C
2. The length of a rectangle is decreased to half, while its breadth is increased 3 times. Calculate the percentage change in area of the rectangle?
Options:
A. 25%
B. 50%
C. 72%
D. 20%
Solution:
Let the original length = l
Let the original breadth = b
Original Area = l * b
New length = $\frac{l}{2}$
New breadth = 3b
New area = $\frac{l}{2}$ x 3b = $\frac{3}{2}lb$
Increase in percentage = $\frac{New\; Area\; - Original\; Area\;}{Original\; Area\;}$ x $100$
= $\frac{(\frac{3}{2}lb)-lb}{lb}$
Increase in percentage = $\frac{100}{2}$ = 50%
Correct option: B
3. If the length of a rectangle is increased by 25% and the width is decreased by 20%, then find the area of the rectangle?
Options:
A. 25% increase
B. 50 % decrease
C. remains unchanged
D. 10 % increase
Solution:
Let the original length = l
Let the original breadth = b
Original Area = l * b
New length = $\frac{125}{100}l$
New breadth = $\frac{80}{100}b$
New area = $\frac{125}{100}$ x $\frac{80}{100}$
New area = $\frac{5}{4}$ x $\frac{4}{5}$
Therefore, original and new area are same. It means the area remains unchanged.
Correct option: C
1: Calculate the cost of making a garden at one meter boundary around a rectangular plot at the rate of Rs. 20/ sq m? The perimeter of the plot is 340 meters.
Options:
A. Rs. 6810
B. Rs. 6880
B. Rs. 6880
D. Rs. 6600
Solution:
Perimeter of the rectangle = 2 (l+b)
So, 340 = 2 (l + b)
Now we have to make garden in one meter boundary
Therefore, we will add 4 to the perimeter
340 + 4 =344
Therefore, required cost = 20 * 344 = 6880
Correct option: B
2 Ajit has a plot of area equal to 361 sq ft. He thought to build a fencing around the four sides of the plot. The cost per foot of building the fence is Rs. 50. Calculate the total cost of building a fencing around the plot?
Options:
A. Rs. 3710
B. Rs. 3890
C. Rs. 3800
D. Rs. 3580
Solution:
Area of square = a = 361
s = 19
Length of the fence = Perimeter of the plot = 4s = 4 * 19 = 76
Therefore, cost of building the fence = 76 * 50 = Rs. 3800.
Correct option: C
3: A rectangular wall whose length is 10 m more than its breadth. The cost of painting the wall is at Rs 30 per meter is Rs. 2100, what is the length of the wall in meters?
Options:
A. 22.5m
B. 17.5m
C. 30 m
D. 20 m
Solution:
Breadth of the wall = x
Length of the wall = x + 10
Perimeter of the rectangular wall = $\frac{2100}{30}$ = 70 m
$2 (l+b) = 70$
2 (x + 10 + x) = 70
2 (2x + 10) = 70
2x + 10 = 35
2x = 25
x = 12.5
Length = x+ 10 = 12.5 + 10 = 22.5m
Breadth = 12.5m
Correct option: A