Amigos.Tech

Easy Areas : 

These problems can be solved by knowing basic area formulas.

Question 1

Messrs. Siva Constructions, leading agents in Chennai prepared models of their lands in the shape of a rectangle and triangle. They made models having same area. The length and width of rectangle model are 24 inches and 8 inches respectively. The base of the triangle model is 16 inches. What is the altitude of triangle model from the base to the top?

a) 24 inches b) 8 inches c) 20 inches d) 32 inches

Answer : a) 24 inches

Solution :

Area of rectangle model -- length x breadth = 24 x 8 = 192 sq. inches.
Area of triangle model is also 192 sq.inches.
Its base - 16 inches
Area of a triangle - 1/2 x base x height
1/2 x 16 x height = 192
Height = (192 x 2) / 16 = 24 inches.

Question 2

Fisher-Price, leading toy manufacturers made a rectangle toy and triangle toy having same area. The length of the rectangle was 30 inches. The triangle toy’s height was 36 inches. How will you express the base y of the triangle as a function of the breadth x of the rectangle ?

a. 20x/3 b. 10x/3 c. 16x d. 22x

Answer : b. 10x/3

Solution :

Base of the triangle = y.
Breadth of the rectangle = x.
Area of the rectangle = length x breadth = 30x
Area of the triangle = 1/2 x base x height = 36y/2 = 18y
Equating the areas of triangle and rectangle, we get, 30x = 18y or y = 30x/18 = 10x/3

Question 3

Ideal Toy company, New York brought out two models – one rectangle and another hexagon in shape. The area of the two are same. The base and height of the triangle are 48” and √3” respectively. Find the length of each of the sides of the hexagon.

a) 2” b) 4” c) 24” d) 8”

Answer : b) 4”

Solution :

Area of triangle = 1/2 x base x height = 1/2 x 48 x √3 = 24√3 sq. inches
Since, the areas of triangle and hexagon are equal , Area of hexagon = 24√3 sq. inches ....(1)
If the side of hexagon is x inches, then its area = (3√3/2 )r2 ...(2)
Since equations 1 and 2 equal,
24√3 = (3√3/2 )r2
16 = r2
Or r = 4 inch