Learn and practice the chapter "Area and Perimeter" with these solved Aptitude Questions and Answers. Each question in the topic is accompanied by a clear and easy explanation, diagrams, formulae, shortcuts and tricks that help in understanding the concept.
Use of Area and Perimeter Questions
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1. A triangular area has to be painted with neon paint. The cost of painting is Rs 80 per sq km.
The sides of the area are 8 km, 10 km and 6 km. Find the cost that will be incurred on painting it.
a. Rs. 1920
b. Rs. 2560
c. Rs. 3840
d. Rs. 38400
Answer: a. Rs. 1920
Explanation:
Tip:
Sides of triangle = a, b and c
Area = 2s(s-a)(s-b)(s-c)
Here value of s =
a+b+c
2
s =
a+b+c
=
8+6+10
= 12
2
2
Area = 2s(s-a)(s-b)(s-c) = 212(12-6)(12-10)(12-8)
∴ Area = 212 x 6 x 2 x 4 = 24 sq.km Cost = Rate x Area = 80 x 24 = Rs. 1920
2. Three triangles, △LMN, △PQR and △CDE are formed in such a way that the inside triangle is formed by joining the midpoints of the sides of outside triangle. △LMN is the outermost triangle while △CDE is the innermost triangle. The length of the sides of inner most triangle are CD = 3, DE = 8 and CE = 4. Find the perimeter of the outermost triangle.
a. 30
b. 60
c. 72
d. 90
Answer: b. 60
Explanation:
We can draw the triangles to understand the sum better
Tip:
When you join midpoints of sides of a triangle and form a smaller triangle, then
Bigger △'s Area = 2 x Area of Smaller △
Bigger △'s Perimeter = 2 x Perimeter of Smaller △
∴ Perimeter of △PQR = 2 x Perimeter of △CDE = 2(3+8+4) = 30 Perimeter of △LMN = 2 x Perimeter of △PQR = 2 x 30 = 60
3. The length and breadth of a rectangular piece of fabric are in the ratio 7:4. The length of the fabric is 15 m more than that of the breadth. Find the area that this fabric would cover.
a. 450 sq.m.
b. 700 sq.m.
c. 850 sq.m.
d. 900 sq.m.
Answer: b. 700 sq.m.
Explanation:
Let the common factor be K
∴ Length = 7K and Breadth = 4K
Also, 4K+15m = 7K
∴ K = 5 ∴ Area of Rectangular ground = Length x Breadth = 7K x 4K = 35 x 20 = 700 sq.m.
4. A rectangular piece of paper has an area 840 sq. cm. The length of the side is 48 cm. The
rectangle is stretched such that its area becomes 2
6
times original rectangle. The only dimension
7
that changes is the breadth of the rectangle. Find the perimeter of the new rectangle.
a. 1.69 m
b. 1.85 m
c. 1.96 m
d. 2.25 m
Answer: c. 1.96 m
Explanation:
New area = 840 x 2
6
= 840 x
20
= 2400 sq.cm
7
7
Area of Rectangle = length x breadth
New Breadth =
New Area
=
2400
= 50 cm
Length
48
Perimeter of new margin = 2(length + new breadth) = 2(48 + 50) = 196cm = 1.96m
5. Sheetal has a rectangular piece of cloth with dimensions 20 m and 15 m. She wants to paint a border of breadth 4 m inside the four sides of the rectangle. The paint would cost her Rs 6 per sq m. Find the cost of painting the complete border.
a. Rs. 1083
b. Rs. 1296
c. Rs. 1500
d. Rs. 1548
Answer: b. Rs. 1296
Explanation:
The fabric and the border can be drawn as follows
Paint Area = Total area - Non-Paint area
Subtracting width of the border from all sides we get,
Length = 20 - 4 - 4 = 12
Breadth = 15 - 4 - 4 = 7
∴ Paint Area = (20 x 15) - (12 x 7) = 300 - 84 = 216 Total Cost of painting the border = Rate x Area = 6 x 216 = Rs. 1296
