Calculate the Area of ABFE: Rectangle with Points at FC=1.5cm, EC=5cm, DE=3cm

Question

The quadrilateral ABCD is a rectangle.

Points E and F are located on sides DC and BC respectively.

FC = 1.5 cm
EC = 5 cm
DE = 3 cm

AD = 4 cm

Calculate the area of the quadrilateral ABFE.

00:21 We're going to calculate the area of the square A, B, F, E.

00:26 First off, let's find the area of the rectangle.

00:30 It's side 4 multiplied by side, open parentheses, 3 plus 5, close parentheses.

00:36 And that's how we get the area of the rectangle.

00:40 Next, let's calculate the area of triangle A, D, E.

00:44 We take the height 4, multiply it by base 3, and then divide by 2.

00:50 Now, we'll find the area of triangle F, E, C using the same steps.

00:58 We have the area for triangle F, E, C.

01:07 To find the area of square A, B, F, E, subtract the areas of the triangles from the rectangle's area.

01:14 Let's plug in our numbers and solve to find the area.

01:18 And that's our solution!

Let's calculate the side DC:

$3+5=8$

Now we can calculate the area of square ABCD:

$4\times8=32$

Let's calculate the area of triangle ADE:

$\frac{4\times3}{2}=\frac{12}{2}=6$

Let's calculate the area of triangle FCE:

$\frac{5\times1.5}{2}=\frac{7.5}{2}=3.75$

Now let's calculate the area of AEFB by subtracting the other areas we found:

$AEFB=32-6-3.75=22.25$

22.25