Ratio and proportion

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns around and heads back to the starting point where he meets the runner who is just finishing his first circuit. Find the ratio of their speeds.

What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?

Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?

Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant and in the ratio 5 to 4. The buses travel to and fro between the towns. What milestones are at Shipton and Veston?

Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.

Which exact dilution ratios can you make using only 2 dilutions?

Use the grids to draw pictures to different scales.

Sam's grandmother has an old recipe for cherry buns. She has enough mixture to put 45 grams in each of 12 paper cake cases. What was the weight of one egg?