The trapezoid DECB forms part of triangle ABC.
AB = 6 cm
AC = 10 cm
Calculate the area of the trapezoid DECB, given that DE divides both AB and AC in half.
DE crosses AB and AC, that is to say:
AD=DB=21AB=21×6=3
AE=EC=21AC=21×10=5
Now let's look at triangle ADE, two sides of which we have already calculated.
Now we can find the third side DE using the Pythagorean theorem:
AD2+DE2=AE2
We substitute our values into the formula:
32+DE2=52
9+DE2=25
DE2=25−9
DE2=16
We extract the root:
DE=16=4
Now let's look at triangle ABC, two sides of which we have already calculated.
Now we can find the third side (BC) using the Pythagorean theorem:
AB2+BC2=AC2
We substitute our values into the formula:
62+BC2=102
36+BC2=100
BC2=100−36
BC2=64
We extract the root:
BC=64=8
Now we have all the data needed to calculate the area of the trapezoid DECB using the formula:
(base + base) multiplied by the height divided by 2:
Keep in mind that the height in the trapezoid is DB.
S=2(4+8)×3
S=212×3=236=18