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

Q: Why do I need to subtract the triangle areas?

You want the area of quadrilateral ABFE, not the whole rectangle ABCD. The triangles ADE and FCE are the unwanted parts that need to be removed from the total rectangle area.

Q: How do I know which triangles to subtract?

Look at the diagram! Triangle ADE and triangle FCE are the two corners that are not part of quadrilateral ABFE. Everything else stays in your final shape.

Q: Can I calculate ABFE directly without subtraction?

It's much harder! The subtraction method is easier because rectangles and right triangles have simple area formulas. Direct calculation would require more complex geometry.

Q: What if I get the triangle area formula wrong?

Remember: Triangle area = $ \frac{1}{2} \times \text{base} \times \text{height} $. For right triangles, use the two perpendicular sides as base and height.

Q: How do I check if my final answer makes sense?

Your answer should be less than the rectangle area (32 cm²) but greater than half the rectangle area. Since 22.25 is between 16 and 32, it makes sense!

Rectangle Areas with Composite Shape Subtraction

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.

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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.

Step-by-step 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:

$AEFB=32-6-3.75=22.25$

Final Answer

22.25

Key Points to Remember

Essential concepts to master this topic

Rectangle Area: Find DC = DE + EC = 3 + 5 = 8 cm
Subtraction Method: ABFE = Rectangle ABCD - Triangle ADE - Triangle FCE
Check: Triangle areas: ADE = 6 cm², FCE = 3.75 cm², sum = 9.75 cm² ✓

Common Mistakes

Avoid these frequent errors

Adding triangle areas instead of subtracting them
Don't add triangle areas ADE and FCE to the rectangle area = 41.75 cm²! This counts the triangles as extra area instead of removing unwanted parts. Always subtract unwanted triangle areas from the total rectangle area.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle below.

Side AB is 2 cm long and side BC has a length of 7 cm.

What is the perimeter of the rectangle?

FAQ

Everything you need to know about this question

Why do I need to subtract the triangle areas?

You want the area of quadrilateral ABFE, not the whole rectangle ABCD. The triangles ADE and FCE are the unwanted parts that need to be removed from the total rectangle area.

How do I know which triangles to subtract?

Look at the diagram! Triangle ADE and triangle FCE are the two corners that are not part of quadrilateral ABFE. Everything else stays in your final shape.

Can I calculate ABFE directly without subtraction?

It's much harder! The subtraction method is easier because rectangles and right triangles have simple area formulas. Direct calculation would require more complex geometry.

What if I get the triangle area formula wrong?

Remember: Triangle area = $\frac{1}{2} \times \text{base} \times \text{height}$ . For right triangles, use the two perpendicular sides as base and height.

How do I check if my final answer makes sense?

Your answer should be less than the rectangle area (32 cm²) but greater than half the rectangle area. Since 22.25 is between 16 and 32, it makes sense!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Rectangles questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

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

Rectangle Areas with Composite Shape Subtraction

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I need to subtract the triangle areas?

How do I know which triangles to subtract?

Can I calculate ABFE directly without subtraction?

What if I get the triangle area formula wrong?

How do I check if my final answer makes sense?

🌟 Unlock Your Math Potential

More Questions

Area of a Rectangle

Calculate the Area of a Modified Rectangle: 6cm × 7cm with Erased Segment

Calculate Rectangle Area: Using Given Dimensions 8 and 17

Rectangle-Square Area Ratio: Find Area When Square = 16 cm²

Find Rectangle Area: Using Triangle Area 8X and Side Length X+4

Area of a Triangle

Calculate Triangle Side AC and Height AE: Given Area 56 cm² and Side 4⅔ cm

Calculate Triangle DEF: Finding Height DG and Area with 8cm Base

Triangle ABC: Finding AB Length When AD=6, CE=3, and CB=5

Triangle Area Calculation: Finding Area with Base 4 and Height 8.5