Given that the area of a trapezium is 𝐴 equals a half ℎ times 𝑎 plus 𝑏, find the value of 𝐴 when ℎ is equal to four centimetres, 𝑎 is equal to three over two centimetres, and 𝑏 is equal to five over two centimetres.
Well, before we do this question, let’s just draw a quick diagram. Here’s our trapezium. 𝑎 and 𝑏 are the parallel sides and ℎ is the perpendicular distance between them. Now, it’s not an accurate diagram, and it’s not to scale. But if we just fill in those dimensions there, 𝑎 is three over two centimetres, 𝑏 is five over two centimetres, and ℎ is four centimetres. Now, let’s go ahead and calculate the area.
So first of all, let’s write down the formula: 𝐴 is equal to half times ℎ times 𝑎 plus 𝑏. Now, we can replace each of those individual letters with the values that we were given: ℎ is four, 𝑎 is three over two, and 𝑏 was five over two. Now before we go on, let’s just do a quick check. We can see that 𝑎 was in centimetres, 𝑏 was in centimetres, and ℎ was in centimetres, so that all the same units. So we don’t have to make any adjustments.
Let’s first evaluate the contents of the parenthesis here: three over two plus five over two, they’re both fractions with two as a denominator, and three twos plus five twos make eight twos or eight over two, and in fact eight over two means eight divided by two, and eight divided by two is four. So let’s write that in.
Now we know that the area is equal to half times four times four. Well, a half times four is two, so that becomes two times four and two times four is eight. Now, finally given that our lengths were given in centimetres, that means the area is given in centimetres squared or square centimetres. So our answer is 𝐴 is equal to eight square centimetres.