Calculate Rectangle Area: Finding ABGE with Given Measurements 5cm and 3cm

Question

The trapezoid ABCD and the rectangle ABGE are shown in the figure below.

Given in cm:

AB = 5

BC = 5

GC = 3

Calculate the area of the rectangle ABGE.

555555333AAABBBCCCDDDEEEGGG

Video Solution

Solution Steps

00:00 Calculate the area of rectangle ABGE
00:03 We will use the Pythagorean theorem in triangle BCG
00:08 We will substitute appropriate values and solve to find height BG
00:22 We will isolate BG
00:28 This is the height BG which is also a side in the rectangle
00:33 We'll calculate the rectangle's area by multiplying side(4) by side(5)
00:40 And this is the solution to the question

Step-by-Step Solution

Let's calculate side BG using the Pythagorean theorem:

BG2+GC2=BC2 BG^2+GC^2=BC^2

We'll substitute the known data:

BG2+32=52 BG^2+3^2=5^2

BG2+9=25 BG^2+9=25

BG2=16 BG^2=16

BG=16=4 BG=\sqrt{16}=4

Now we can calculate the area of rectangle ABGE since we have the length and width:

5×4=20 5\times4=20

Answer

20