Test: Area & Perimeter - 1 - CDS MCQ

Let the area of backyard be x² this year and y² last year.

X²- Y² = 131
(X+Y) (X-Y) = 131

Now, 131 is a prime number (a unique one too. Check out its properties on Google). Also, always identify the prime number given in a question. Might be helpful in cracking the solution.

⇒ (X+Y) (X-Y) = 131 x 1
⇒ X+Y = 131
⇒ X-Y = 1
⇒ 2X = 132
⇒ X = 66 and Y = 65

∴ Number of tomatoes produced this year = 66² = 4356

Choice (C) is therefore, the correct answer.
Correct Answer: 4356

If we write the infinite series of area of squares:
= 4² + (2√2)² + 2² + ……. infinite

Since it is a decreasing series sum of infinite terms can be approximated.
= 16 + 8 + 4 +………infinite

Since neither angles nor sides are given in the question, immediately the sum of angles of pentagon should come in mind. To use it,

We know the area of the sectors of a circle is given as:

Note: The above concept is applicable for a polygon of n sides.

Choice (B) is therefore, the correct answer.
Correct Answer: 1.5πr²

Area of the circle=πr²

2464 = 22/7 * r²

Radius of the circle=28 cm

Circumference of the circle=2 * π* r =2 * 22/7 * 28 

= 176 cm

Breadth of the rectangle=6/7 * 28=24 cm

Perimeter of the rectangle=2 * (l + b)

176 = 2 * (l + 24)

Length of the rectangle = 64 cm

Area of the rectangle = l * b = 24 * 64 = 1536 cm² 

area=1/2×d×(h₁+h₂)
=1/2×24×(12+6)
=12(18)
=216 m²

Let ABCDEFGH be the cube of side a and O be the centre of the hemisphere.

AC = √2 a

OD = OC = R
Let P be the mid-point of AC

OP = a

Now in  Δ AOC

The distance from any vertex at the base of the cube to the vertex that is perpendicular along height to the diametrically opposite vertex is required.
We have to calculate DF.

Area of a triangle = r * s

Where r is the inradius and s is the semi perimeter of the triangle.

Area of triangle = 2.5 * 28/2 = 35 cm²

Length of the first carpet = (1.44)(6) = 8.64 cm

Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)

= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m

Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40

Equate the area of the square ABCD and triangle PDC and find a relation between the slant height and the length of the base of the pyramid

Let the radius of the wheel be = p
Then 5000 × 2pr = 1100000 cm fi r = 35 cm

In 4 days, the short hand covers its circumference
4 × 2 = 8 times long hand covers its circumference
4 × 24 = 96 times
Then they will cover a total distance of:-
(2 × p × 4)8 + (2 × p × 6)96 fi 3818.24 cm