Area of a Triangle (Leaving Cert Mathematics): Flashcards

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Area of a Triangle
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What is the area formula when one vertex is at the origin?

12∣x1y2−x2y1∣\frac{1}{2}|x_1y_2 - x_2y_1|

What do vertical lines mean in ∣x1y2−x2y1∣|x_1y_2 - x_2y_1|?

Absolute value

When to use 12∣x1y2−x2y1∣\frac{1}{2}|x_1y_2 - x_2y_1| directly?

When one vertex is at origin (0,0)

How do you cross multiply in the triangle area formula?

Multiply x1x_1 by y2y_2 and x2x_2 by y1y_1

After cross multiplication, what operation?

Find difference between products

Why take absolute value in area formula?

To ensure area is always positive

Final step after ∣x1y2−x2y1∣|x_1y_2 - x_2y_1|

Multiply by 12\frac{1}{2}

Method when no vertex at origin

Translate triangle so one vertex moves to (0,0)

Does translation change triangle area?

No

Can you choose any vertex to move to origin?

Yes, result will be same

Common mistake #1 in area calculation

Forgetting to take absolute value

Common mistake #2 in area calculation

Forgetting to multiply by 12\frac{1}{2}

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