Exercise 13.6

1. A path 2.5 m wide is running around a square field whose side is 45 m. Determine the area of the path.

Answer:

Side of the square field (outer square) = m

Area of the outer square = side × side = × = m²

Width of the path = m

Side of the inner square (field without path) = 45 - (2 × )

Side = 45 - = m

Area of the inner square = side × side = × = m²

Area of the path = Area of outer square - Area of inner square

Area of the path = -

Area of the path = m²

2. The central hall of a school is 18m long and 12.5 m wide. A carpet is to be laid on the floor leaving a strip 50 cm wide near the walls, uncovered. Find the area of the carpet and also the uncovered portion?

Answer:

Length of the hall (L) = m

Width of the hall (B) = m

Area of the hall = L × B = 18 × 12.5 = m²

Width of the uncovered strip = 50 cm = m

Length of the carpet = 18 - (2 × ) = 18 - = m

Width of the carpet = 12.5 - (2 × ) = 12.5 - = m

Area of the carpet = length of carpet × width of carpet = × = m²

Area of the uncovered portion = Area of hall - Area of carpet

Area of the uncovered portion = -

Area of the uncovered portion = m²

3. The length of the side of a grassy square plot is 80 m. Two walking paths each 4 m wide are constructed parallel to the sides of the plot such that they cut each other at the centre of the plot. Determine the area of the paths.

Answer:

Side of the square plot (L) = m

Width of the paths (w) = m

Area of the path along length = L × w = × = m²

Area of the path along width = L × w = × = m²

Area of the common square (intersection) = w × w = × = m²

Total area of the paths = (Area of path along length + Area of path along width) - Area of common square

Total area of the paths = ( + ) -

Total area of the paths = -

Total area of the paths = m²

4. A verandah 2 m wide is constructed all around a room of dimensions 8 m × 5 m. Find the area of the verandah

Answer:

Length of the room (l) = m

Width of the room (b) = m

Area of the room = l × b = × = m²

Width of the verandah = m

Length of the room with verandah (L) = 8 + (2 × ) = 8 + = m

Width of the room with verandah (B) = 5 + (2 × ) = 5 + = m

Area of the room with verandah = L × B = × = m²

Area of the verandah = Area of room with verandah - Area of the room

Area of the verandah = -

Area of the verandah = m²

5. The length of a rectangular park is 700 m and its breadth is 300 m. Two crossroads, each of width 10 m, cut the centre of a rectangular park and are parallel to its sides. Find the area of the roads. Also, find the area of the park excluding the area of the crossroads.

Answer:

Length of the park (L) = m

Breadth of the park (B) = m

Width of crossroads (w) = m

Area of road parallel to length = L × w = × = m²

Area of road parallel to breadth = B × w = × = m²

Area of common square (intersection) = w × w = × = m²

Area of the roads = (Area of road parallel to length + Area of road parallel to breadth) - Area of common square

Area of the roads = ( + ) -

Area of the roads = -

Area of the roads = m²

Area of the park = L × B = × = m²

Area of the park excluding the area of the crossroads = Area of the park - Area of the roads

Area of the park excluding the area of the crossroads = -

Area of the park excluding the area of the crossroads = m²