Practice

Question 1

Mrs Tan pins three identical equilateral triangular bunting flags, Flag 1, Flag 2 and Flag 3, along a straight horizontal string. Each flag points upwards and its bottom edge lies flat on the string. Flag 1 is on the left, Flag 2 is in the middle and Flag 3 is on the right. Flag 2 overlaps Flag 1 and also overlaps Flag 3, but Flag 1 and Flag 3 do not touch each other. On the string: • the distance from the left corner of Flag 1 to the left corner of Flag 2 is 15 cm, • the distance from the left corner of Flag 3 to the right corner of Flag 2 is 4 cm, • the distance from the right corner of Flag 1 to the right corner of Flag 3 is 33 cm. The shaded parts are the part of Flag 1 not covered by Flag 2 and the part of Flag 3 not covered by Flag 2. (a) Find the length of one side of a flag. (b) Find the total perimeter of the two shaded parts.

Work it out on paper, then check below. ▶ See the working

Question 2

Mr Kumar stands three identical equilateral triangular wooden blocks, Block A, Block B and Block C, upright in a straight groove on his workbench. Each block rests with its bottom edge lying flat along the groove. Block A is on the left, Block B is in the middle and Block C is on the right. Block B overlaps Block A when seen from the front, and Block B also overlaps Block C, but Block A and Block C do not overlap each other. Measured along the groove: • the distance from the left corner of Block A to the left corner of Block B is 25 cm, • the distance from the left corner of Block C to the right corner of Block B is 5 cm, • the distance from the right corner of Block A to the right corner of Block C is 52 cm. The shaded parts are the part of Block A that is not hidden by Block B, and the part of Block C that is not hidden by Block B. (a) Find the length of one side of a block. (b) Find the total perimeter of the two shaded parts.

Work it out on paper, then check below. ▶ See the working