Area (Parallelograms, Trapeziums, Polygons): Practice Questions

A parallelogram has a base of \(12 \text{ cm}\) and a perpendicular height of \(7 \text{ cm}\). What is the area of this parallelogram?

A square with a side length of \(8 \text{ cm}\) has two identical right-angled triangles removed from its corners. Each triangle has a base of \(2 \text{ cm}\) and a height of \(2 \text{ cm}\). What is the area of the remaining polygon?

A designer is working on a banner shaped like a rectangle measuring \(45 \text{ cm}\) by \(20 \text{ cm}\). A decoration in the shape of a trapezium is cut out from the banner, spanning from the top edge to the bottom edge. The parallel sides of the trapezium decoration measure \(5 \text{ cm}\) and \(7 \text{ cm}\) along the long edges of the banner. What is the area of the banner that remains after the decoration is removed?

A trapezium has parallel sides of length \( 14 \text{ cm} \) and \( 22 \text{ cm} \). If its perpendicular height is \( 10 \text{ cm} \), what is its area?

The area of a trapezium is \(56 \text{ cm}^2\). The lengths of its parallel sides are \(6 \text{ cm}\) and \(8 \text{ cm}\). What is the perpendicular height of the trapezium?

The area of a parallelogram is \(60 \text{ cm}^2\). If its base is \(10 \text{ cm}\), what is its perpendicular height?

A large trapezium has parallel sides of \(25 \text{ cm}\) and \(35 \text{ cm}\), and a perpendicular height of \(12 \text{ cm}\). A parallelogram with a base of \(8 \text{ cm}\) and a perpendicular height of \(5 \text{ cm}\) is cut out from the center of the trapezium. What is the area of the remaining shape in square centimetres?

A symmetrical pentagonal plaque has a total area of \(234 \text{ cm}^2\). It is composed of a trapezium at the bottom and an isosceles triangle on top. The trapezium has a lower base of \(24 \text{ cm}\), an upper base of \(12 \text{ cm}\), and a perpendicular height of \(10 \text{ cm}\). The isosceles triangle sits on top of the \(12 \text{ cm}\) upper base. What is the perpendicular height of the triangle in centimetres?

Compare the areas of two different fields. Field A is a parallelogram with a base of \(10\) m and a height of \(6\) m. Field B is a trapezium with parallel sides of \(7\) m and \(9\) m, and a height of \(5\) m. Which field has a larger area?

A logo is made up of a parallelogram and a trapezium. The parallelogram has a base of \(12\) cm and a height of \(7\) cm. The trapezium is attached to one side of the parallelogram. One of its parallel sides is \(12\) cm (shared with the parallelogram) and the other parallel side is \(18\) cm. If the total area of the logo is \(147\) cm\(^2\), what is the perpendicular height of the trapezium?