Pythagoras test questions

1

A composite shape is made up of a square and a right angled triangle. It has measurements as shown.

Square and right angle triangle. Square 9m tall. Base of shape 13.6m long.

Calculate the perimeter of the shape.

2

A dog’s toy is in the shape of a tetrahedron. Each face of the toy is an equilateral triangle of side \(14cm\).

Calculate the area of one of these faces (giving your answer to the nearest square centimetre).

Face of tetrahedron 14cm sides

3

Calculate the length of side \(x\)

Quadrilateral split into two right angled triangles. Triangle one 7cm by 5cm by hypotenuse. Triangle two 6cm by triangle one hypotenuse by x

4

A garden has two rectangular sections as shown. These have the same measurements.

Two gardens 11m by 6.3m. Second garden is rotated 90 degrees and aligned on right. Line y connects bottom left corners of each garden.

Calculate the length of \(y\).