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

Q: How do I identify which triangles to subtract from the rectangle?

Look for any shaded or unshaded regions that aren't part of the final shape. In this problem, triangles ABC and HGD are the blue regions that must be subtracted from the total rectangle area.

Q: Why is the triangle area formula divided by 2?

A triangle is exactly half the area of a rectangle with the same base and height. So $ \text{Area} = \frac{\text{base} \times \text{height}}{2} $ gives us the correct triangular area.

Q: What if I get a decimal answer?

Decimal answers are completely normal for area problems! 43.5 cm² is a valid area measurement. Just make sure to include the proper units (cm², m², etc.) in your final answer.

Composite Area Calculation with Triangle Subtraction

The shape below consists of a rectangle from which the line segment BH has been erased.

AB=6
AC=7
EF=3
CD=12
BE=3

Calculate the area of the shape shaded orange.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:19 Let's find the area of the brown shape.

00:22 First, we calculate the area of triangle A B C.

00:26 Multiply height 7, by base 6, then divide by 2.

00:32 That's the area of triangle A B C.

00:35 Now, use the same formula to find the area of triangle H G D.

00:42 This gives us the area of triangle H G D.

00:49 Next, complete B H into a square.

00:56 Calculate its area as side 3, squared.

01:00 This is the area of square B H F E.

01:04 Now, find the area of large rectangle A G D C.

01:09 Multiply side 12, by side 7.

01:12 That's the area of rectangle A G D C.

01:17 To find the area of the brown shape, we subtract areas.

01:21 Subtract areas of both triangles and the square from the rectangle's area.

01:28 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The shape below consists of a rectangle from which the line segment BH has been erased.

AB=6
AC=7
EF=3
CD=12
BE=3

Calculate the area of the shape shaded orange.

Step-by-step solution

Let's first calculate the area of triangle ABC:

$\frac{6\times7}{2}=\frac{42}{2}=21$

Since the shape before us is a rectangle, we can claim that:

AC=GD=7

Now let's calculate the area of triangle HGD:

$\frac{7\times3}{2}=\frac{21}{2}=10.5$

Let's draw an imaginary line between B and H to get square BEFH where each side equals 3 cm.

Let's calculate the area of BEFH:

$3\times3=9$

Let's calculate the area of rectangle ACDG:

$7\times12=84$

Now we can calculate the area of the brown shape by subtracting the other areas we found:

Final Answer

43.5 cm

Key Points to Remember

Essential concepts to master this topic

Strategy: Calculate total rectangle area, then subtract removed triangular sections
Method: Rectangle area (7×12=84) minus triangle areas like $\frac{6\times7}{2}=21$
Verification: Add all component areas back together to check against original rectangle ✓

Common Mistakes

Avoid these frequent errors

Forgetting to subtract all triangular sections
Don't just subtract triangle ABC and ignore triangle HGD = incomplete calculation! This leaves extra area that shouldn't be counted. Always identify and subtract every triangular section that was removed from the original rectangle.

Practice Quiz

Test your knowledge with interactive questions

Angle A is equal to 30°.
Angle B is equal to 60°.
Angle C is equal to 90°.

Can these angles form a triangle?

FAQ

Everything you need to know about this question

How do I identify which triangles to subtract from the rectangle?

Look for any shaded or unshaded regions that aren't part of the final shape. In this problem, triangles ABC and HGD are the blue regions that must be subtracted from the total rectangle area.

Why is the triangle area formula divided by 2?

A triangle is exactly half the area of a rectangle with the same base and height. So $\text{Area} = \frac{\text{base} \times \text{height}}{2}$ gives us the correct triangular area.

How do I find the dimensions of each triangle?

Use the given measurements! For triangle ABC: base AB=6, height AC=7. For triangle HGD: base HG=3, height GD=7. Always check the diagram labels to identify the correct measurements.

What if I get a decimal answer?

Decimal answers are completely normal for area problems! 43.5 cm² is a valid area measurement. Just make sure to include the proper units (cm², m², etc.) in your final answer.

Can I solve this by adding shapes instead of subtracting?

Yes! You could break the orange shape into smaller rectangles and triangles, then add their areas together. Both methods should give you the same answer of 43.5 cm².

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

Composite Area Calculation with Triangle 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

How do I identify which triangles to subtract from the rectangle?

Why is the triangle area formula divided by 2?

How do I find the dimensions of each triangle?

What if I get a decimal answer?

Can I solve this by adding shapes instead of subtracting?

🌟 Unlock Your Math Potential

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