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 the rectangle ABGE
00:03 Apply the Pythagorean theorem to the triangle BCG
00:08 Substitute in the relevant values and solve to find height BG
00:22 Isolate BG
00:28 This is the height BG which is also a side in the rectangle
00:33 Calculate the rectangle's area by multiplying side(4) by side(5)
00:40 This is the solution

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

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The Area of a Triangle Calculating the Area of a Rectangle Area Area of Equilateral Triangles Area of a Scalene Triangle Area of Isosceles Triangles The Pythagorean Theorem Rectangle Triangle Area of a right triangle Areas of Polygons for 7th Grade How do we calculate the area of complex shapes? How to calculate the area of a triangle using trigonometry?

Question Types

Area of a Rectangle: Using additional geometric shapes Area of a Rectangle: Using Pythagoras' theorem Area of a Triangle: Using additional geometric shapes Area of a Triangle: Using Pythagoras' theorem Using the Pythagorean Theorem: Using additional geometric shapes Using the Pythagorean Theorem: Using Pythagoras' theorem