Geometry and measures worksheet — GCSE Higher

1.A sector of a circle has radius 10 cm and angle 150°. Using π = 3.14, work out the perimeter of the sector, to 1 decimal place.

2.A line passes through the points (1, 2) and (3, 6). The line is reflected in the x-axis, and the image is then translated by the vector (2, 0). Work out the gradient of the image line after both transformations.

3.Point E is at (4, 2). It is rotated 180° about the point (1, 1). Work out the coordinates of the image of point E.

4.In triangle ABC, AB = AC = 9 cm and angle ABC = angle ACB = 65°. Work out the area of triangle ABC. Give your answer to 1 decimal place.

5.A(1, 2), B(5, 2) and C(5, 6) are three of the four vertices of a square ABCD. Work out the coordinates of D.

6.Two similar ponds have perimeters in the ratio 4 : 11. The perimeter of the larger pond is 88 m. Work out the perimeter of the smaller pond.

7.A window is made from a rectangle with a semicircle on top. The rectangle is 40 cm wide and 60 cm tall. The semicircle has the same width as the rectangle. Work out the total area of the window. Use π = 3.14. Give your answer to the nearest whole number.

8.In triangle ABC, AB = 9 cm, AC = 6 cm and angle BAC = 110°. Work out the length of BC. Give your answer to 1 decimal place.

9.From an external point P, two tangents PA and PB touch a circle with centre O at A and B. Angle AOB = 112°. Work out the size of angle APB.

10.In triangle ABC the angle at C is 90°, AC = 8 cm and the angle at A is 30°. Work out the length of BC. Give your answer to 1 decimal place.

11.Triangle DEF has a right angle at E. Angle DFE = 60° and EF = 9 cm. Work out the exact length of DE.

12.A rhombus-shaped floor tile has sides of length 12 cm and an interior angle of 55°. Work out the area of the tile. Give your answer to 1 decimal place.

13.Two similar company logos are printed at different sizes. The area of the larger logo is 2.25 times the area of the smaller logo. Work out the length scale factor from the smaller logo to the larger logo.

14.In triangle ABC and triangle DEF, the angle at A and the angle at D are both 40°, and the angle at B and the angle at E are both 70°. No side lengths are given. Write down whether the two triangles must be similar, with the reason.

15.Triangle ABC is right-angled at B. Triangle DEF is right-angled at E. AB = DE = 6 cm and AC = DF = 10 cm (AC and DF are the hypotenuses of their triangles). A student says this is not enough information to prove the triangles are congruent, because only two sides are given. Which reason shows the student is wrong?