area of triangle and parallelogram

[frigid night]

I need help with this problem. I'm not the best with geometry so if u are able to simplify ur explaining that would help :) ty

[serene cedar]

lets break down the shape into two triangles

[serene cedar]

whats the formula for the area of a triangle?

[frigid night]

1/2 bh

[serene cedar]

yea

lets focus on the red one first

what do you think is the height

[glass pecan]

In the lower triangle the perpendicular is 5 units and the hypotenuse is 13 units

Hence by utilising Pythagoras theorem you get base² to be 13² - 5² = 12². Hence the base is 12 units

12 units is also the base for the upper triangle hence by the same formula perpendicular ² is 15² - 12²=9². Therefore the perpendicular of the upper triangle is 9 units

Now utilise the area of triangle formula and you get area of upper triangle to be 54 units² and that of lower triangle be 30 units². So the total area is 84 units².

Hope this helps you out@frigid night

[frigid night]

It did, thank u