Maths Problem

here is a correct way:

draw line across from square to arrow to create right angled triangle. Use pythag on this triangle to obtain base of THIS triangle. Take 6 to get length of segment you drew (i.e. approx 3.54). Now use pythag on triangle formed by the segment you drew (3.54), the top bit of the arrow (3) and the unknown side of the triangle we are trying to find the area of, to find it is approx 4.64. Now use cosine rule with respect to an angle of your choice to find this angle (e.g. angle between rectangles is approx 17.46). Then use area of triangle = 1/2×a×b×sinC where the a and b are lengths of the sides next to angle C (i.e. 1/2×10×6×sin 17.46 approx 9).

Easy!

Half base times height works whatever the triangle orientation! It's quite easy to demonstrate for yourself if you draw out the triangle yourself. Using the base as 6 and the height 3 is fine!

0.5 x 6 x 3 = 9 is an exact and straightforward solution to get the area of the triangle. Stop over complicating things.

xiisprime wrote:here is a correct way:

draw line across from square to arrow to create right angled triangle. Use pythag on this triangle to obtain base of THIS triangle. Take 6 to get length of segment you drew (i.e. approx 3.54). Now use pythag on triangle formed by the segment you drew (3.54), the top bit of the arrow (3) and the unknown side of the triangle we are trying to find the area of, to find it is approx 4.64. Now use cosine rule with respect to an angle of your choice to find this angle (e.g. angle between rectangles is approx 17.46). Then use area of triangle = 1/2×a×b×sinC where the a and b are lengths of the sides next to angle C (i.e. 1/2×10×6×sin 17.46 approx 9).

Easy!

Or once you have all three sides you can use Heron's formula to work out the area.

Slartibartfast wrote:Half base times height works whatever the triangle orientation! It's quite easy to demonstrate for yourself if you draw out the triangle yourself. Using the base as 6 and the height 3 is fine!

0.5 x 6 x 3 = 9 is an exact and straightforward solution to get the area of the triangle. Stop over complicating things.

this was looking at 10 being the base, in which case you don't know the height (I showed it was 6×sin17.46 which is approx 1.8).

I also didn't say the other solutions weren't correct, there are often many ways to prove things!