Area Calculation: Finding Parallelogram Area Using Rectangle Area of 35 cm²

Question

ABCD is a parallelogram and AEFD is a rectangle.

AE = 7

The area of AEFD is 35 cm².

CF = 2

What is the area of the parallelogram?

Video Solution

Solution Steps

00:00 Find the area of parallelogram ABDC

00:04 We'll use the formula for rectangle area: side(AE) multiplied by side(ED)

00:11 We'll substitute appropriate values and solve for ED

00:14 Let's isolate ED

00:19 This is the length of side ED

00:26 Opposite sides are equal in a rectangle

00:30 The whole side equals the sum of its parts

00:41 Now we'll use the formula for parallelogram area

00:44 height(ED) multiplied by base(CD)

00:47 We'll substitute appropriate values and solve for the area

00:50 And this is the solution to the problem

Step-by-Step Solution

Let's first calculate the sides of the rectangle:

$AEDF=AE\times ED$

Let's input the known data:

$35=7\times ED$

Let's divide the two legs by 7:

$ED=5$

Since AEDF is a rectangle, we can claim that:

ED=FD=7

Let's calculate side CD:

$2+7=9$

Let's calculate the area of parallelogram ABCD:

$ABCD=CD\times ED$

Let's input the known data:

$ABCD=9\times5=45$

Answer

45 cm².

Related Subjects

Parallelogram Calculating the Area of a Rectangle The area of a parallelogram: what is it and how is it calculated? Area Rectangle

Question Types

Area of a Rectangle: Using additional geometric shapes Area of a Parallelogram: Using additional geometric shapes