Question

If Y=8 cm, what is the area of the blue section of this shape?

Answer 1

Step-by-step explanation

As you can see we have a trapezoid inside a rectangle. The blue section is equivalent to the area of the rectangle that it's not covered by the trapezoid. Then the area of this section is equal to the area of the rectangle less the area of the trapezoid. Then we just need to find the areas of both figures. Remember than the area of a rectangle is given by the product between its height and its base:

`A_r=h\cdot b`

Trapezoids are figures with two parallel sides known as bases. The area of a trapezoid is given by product between the sum of its bases and its height divided by 2:

`A_t=((a+b)\cdot h)/(2)`

Then the area of the rectangle in the picture is given by:

`A_r=10\cdot y=10\cdot8=80`

So it's 80 cm².

The area of the trapezoid considering that its base has the same length as the rectangle is:

`A_t=((4+10)\cdot3)/(2)=(14\cdot3)/(2)=21`

So its area is of 21 cm².

Finally the area of the blue section is given by:

`80-21=59`Answer

Then the answer is 59cm².