Mensuration Test - 1

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

Such questions are all about visualization and ability to write one area in terms of others.

Here, Let the radius of PQRS be 2r 
∴ Radius of each of the smaller circles = 2r/2 = r

∴ Area A can be written as:
A = π (2r)² – 4 x π(r)² (Area of the four smaller circles) + B (since, B has been counted twice in the previous subtraction)

A = 4πr² - 4πr² + B
A = B
A/B = 1

Choice (B) is therefore, the correct answer.
Correct Answer: 1

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