Area (Square, Rectangle, Triangle): Practice Questions

A square floor has a perimeter of \(20\text{ m}\). What is its area?

An L-shaped figure is formed by two rectangles. One rectangle measures \(5\text{ m}\) by \(2\text{ m}\), and the other measures \(3\text{ m}\) by \(4\text{ m}\). What is the total area of the figure?

A rectangular playground has a total area of \(288 \text{ m}^2\). The length of the playground is exactly twice its width. Inside the playground, there are two separate facilities that are not covered by grass: a square sandpit (S) and a triangular flower bed (T).

The side length of the square sandpit is half the width of the rectangular playground.

The height of the triangular flower bed is equal to the side length of the square sandpit, and its base measures \(15 \text{ m}\).

What is the area of the region covered by grass?

A triangle has a base of \(10\text{ cm}\) and a perpendicular height of \(6\text{ cm}\). Calculate its area.

A triangle and a square have the same area. If the side of the square is \(6\text{ cm}\) and the base of the triangle is \(9\text{ cm}\), what is the height of the triangle?

A rectangular garden has a length of \(12\) meters and a width of \(8\) meters. A triangular flower bed is located inside the garden with a base of \(8\) meters (along one of the garden's sides) and a height of \(5\) meters.

What is the area of the garden that is not covered by the flower bed?

A garden plot has a unique shape, formed by a rectangle with two identical right-angled triangles attached to its shorter sides. The rectangle has a length of \(18\) meters and a width of \(10\) meters. Each right-angled triangle has a base equal to the width of the rectangle and a height of \(7\) meters. Inside this garden plot, a square path is built, with a side length of \(5\) meters.

What is the total area of the garden plot that is not covered by the path?

A rectangular plot of land has an area of \(60 \text{ m}^2\). If its length is \(10 \text{ m}\), what is its width?
Also, calculate the area of a triangular flower bed that has a base equal to this width and a height of \(4 \text{ m}\).

A rectangular rug has a length of \(10\) metres and a width of \(7\) metres. A decorative border of uniform width \(1\) metre runs around all four sides of the rug.

a) Calculate the total area of the rug, including the border.

b) Determine the length and width of the inner part of the rug, excluding the border.

c) What is the area of the inner part of the rug?

d) Find the area of the decorative border.

A rectangular park has a length of \(20\) meters and a width of \(10\) meters. Inside this park, there is a square flower bed with sides of \(5\) meters. At one corner of the park, outside the square flower bed, there is a triangular pond with a base of \(8\) meters (along the park's width) and a height of \(6\) meters.

a) Calculate the area of the entire rectangular park.

b) What is the area of the square flower bed?

c) Find the area of the triangular pond.

d) What is the area of the park that is not covered by the square flower bed or the triangular pond?