Below are easy problems dealing with areas. These problems can be solved by knowing basic area formulas.
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
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.
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
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
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”
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