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Geometry Problem Solving Challenges

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Geometry Problem Solving Challenges

Solve each problem and show your working where space is provided. Use centimetres and metres as stated.

Angle Problem Solving

1.A regular decagon has ten equal interior angles. What is the measure of one interior angle?

108°
126°
135°
144°

2.Two parallel lines are crossed by a transversal. One angle is 74°. What is the size of the angle in the matching corresponding position?

16°
74°
106°
180°

3.A triangle has angles of 39° and 68°. Calculate the size of its third angle, x.

Similarity and Scaling

4.Two similar triangles have a smaller-to-larger side ratio of 1:4. The smaller triangle has a perimeter of 15 cm. Find the perimeter of the larger triangle.

5.A 7 cm by 9 cm photograph is enlarged by a linear scale factor of 3. Find the area of the enlarged photograph.

6.Two similar right-angled triangles have hypotenuses of 8 cm and 16 cm. If the shorter leg of the smaller triangle is 5 cm, what is the length of the shorter leg of the larger triangle?

Problem-Solving Challenges

7.A rectangular patio measures 5 m by 8 m. A path of equal width is built around its outside. The patio and path together cover 70 m². Find the path's width.

8.For the patio-and-path problem, describe one equation you could use to calculate the path width and explain why the dimensions each increase by twice that width.

9.Two similar triangles have corresponding sides in the ratio 3:5. A side on the smaller triangle is 12 cm. What is the length of the corresponding side on the larger triangle?

10.A quadrilateral has three interior angles measuring 82°, 97° and 116°. Calculate its fourth interior angle.