Area and Perimeter in the 11+ — Questions, Worked Answers and Practice Papers

{"text":"bold","word":"The Approach"} Imagine if you draw a line where the bushes need planting all the way round then you will get a rectangular shape which would be smaller than the actual garden. Outside of this rectangular shape would be the slabs.  The trick in this problem is to find the size of the new rectangular shape using our superhuman mathematical skills. {"text":"bold","word":"The Solution"} Let's first convert all the numbers into a common unit so that we can make the problem simpler.  {"text":"tip","word":"Always convert the numbers into cm when you see meters (m) and centimetres (cm) in the same question."} So let's convert all of them to cm because we want to avoid using decimals. To convert meters to cms we will multiply it with 100. {"text":"code","word":"Actual garden length in cm = 12 m x 100 = 1200 cm"}{"text":"code","word":"Actual garden width in cm = 8 m x 100 = 800 cm"} Now, let's find out the area that we need to ignore. Each square slab is 1m, i.e. when converted to cms it is 100cm wide and 100cm long. Also, we are asked to leave a gap of 25cm. {"text":"code","word":"Now the length that we need to ignore on the left side is, 100 + 25 = 125 cm. "}{"text":"code","word":"Similarly, we will ignore 125 cm on the right. "} Now, the total length we need to ignore is 125+125 = 250 cm. From the actual garden length, we now need to take away 250 cm to find the length of the new shape, {"text":"code","word":"= 1200 - 250 = 950"} Just like that, we need to take away, 250 cm (top + bottom) from the width, {"text":"code","word":"= 800 - 250 = 550"} The new area that we need to plant the bushes on is,  950 cm long and 550 cm wide. We are going to plant the bushes on the edge of this shape, in other words, we are planting them on the perimeter. So if we know the perimeter then we can find how long is the path that needs planting the bushes. The total length that needs planting is the same as the perimeter of the new shape, which is {"text":"code","word":"= 2 x (950 + 550)"}{"text":"code","word":"= 2 x 1500 = 3000 cm"} We are asked to plant the bushes with a gap of 50 cm, which means that if we find out how many equal parts we can divide the total planting length into, then we can find out how many bushes we need because each bush needs 50 cm space. {"text":"code","word":"= 3000 / 50"}{"text":"code","word":"= 60 equal parts"} If we plant one bush in each part then we need 60 bushes to cover the full length.