Question

Find the area of triangle XYZ​

Answer 1

`\displaystyle A _{XYZ - \text{triangle}} = 24 {cm}^(2)`

Explanation:

we have two right angle triangles

we want to figure out the area of XYZ triangle

we are given the base not the altitude (height) so we need to figure the height of XYZ to figure out the area of XYZ

in that case we can use Pythagoras theorem given by

`\displaystyle {a}^(2) + {b}^(2) = {c}^(2)`

given that, c=5 and b=3 thus

substitute:

`\displaystyle {3}^(2) + {a}^(2) = {5}^(2)`

simplify squares:

`\displaystyle 9 + {a}^(2) = 25`

cancel 9 from both sides:

`\displaystyle {a}^(2) = 16`

square root both sides:

`\displaystyle {a}^{} = 4`

we have figured out the height of XYZ triangle

remember that,

`\displaystyle A _{ \text{triangle}} = (1)/(2) bh`

we have h=4 and b=9+3=12

substitute:

`\displaystyle A _{ \text{triangle}} = (1)/(2) * 12* 4`

reduce fraction:

`\displaystyle A _{ \text{triangle}} = 12* 2`

simplify multiplication:

`\displaystyle A _{ \text{triangle}} = 24`

hence,

the area of triangle XYZ is 24 cm²