 What's the area of this triangle? Pause the video, work it out and click play when you're ready to check. Did you get 35? You probably all know that the area of a triangle is the base multiplied by the perpendicular height. But what if we don't have the perpendicular height? Luckily, we have a backup formula. We need two sides and the angle in between. As with the sine and cosine rule, always start by labelling your sides with big and little, A, Bs and Cs. And just substitute in the values. So what's the area of this triangle? Pause the video, work it out and click play when you're ready. Did you get 4.82 centimetre squared? Make sure you show all of your working to get the marks. Just writing 4.82 wouldn't be good enough. But it won't always be that easy. Sometimes we may need to use our sine and cosine rule knowledge first before we can find the area. Like in this question, we're going to have to find side x before we can find the area. Pause the video, work outside x and then find the area of the triangle. And click play when you're ready. Did you get 143.8 centimetre squared? If you did and you want to skip the explanation, click here. Otherwise, keep watching. We need to use the sine rule. We have 72 and 26 as a complete pair and x and 24 are the half pair. Substitute them into the sine rule and we rearrange to get x equals sine 24 multiplied by 26 over sine 72. Enter that into your calculator and x equals 11.11937 and so on. So now we can find the area. Label your A, B and C's again. Angle C is 84 degrees. So substitute our numbers into the equation and we get the area as 143.8 centimetre squared. So there we have an alternative method for finding the area of a triangle. We quite often need to combine it with our sine rule and cosine rule knowledge. If you're interested to know the proof for this formula, so why this formula works, watch this video.