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.

00:00 Calculate the area of square ABFE

00:03 First, let's calculate the area of the rectangle

00:07 It equals side(4) multiplied by side(3+5)

00:12 This is the area of the rectangle

00:17 Now let's calculate the area of triangle ADE

00:21 (height(4) multiplied by base(3)) divided by 2

00:28 Now let's calculate the area of triangle FEC using the same method

00:37 This is the area of triangle FEC

00:46 The area of square ABFE equals the rectangle's area minus the areas of the triangles

00:50 Let's substitute appropriate values and solve to find the area

00:56 And this is the solution to the problem

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