Area of Triangles
Area of Triangles is a Grade 7 math skill in Big Ideas Math Advanced 2, Chapter 13: Circles and Area, where students apply the formula A = (1/2) * b * h to calculate the area of any triangle given its base and corresponding height, and learn to identify the correct height (perpendicular to the base) for obtuse and right triangles as well as scalene configurations.
Key Concepts
The area of a triangle is one half the base, $b$, times the height, $h$. $$A = \frac{1}{2}bh$$.
Common Questions
What is the formula for the area of a triangle?
A = (1/2) x b x h, where b is the base and h is the height (the perpendicular distance from the base to the opposite vertex). The height must be perpendicular to the chosen base.
How do you find the height of an obtuse triangle?
For an obtuse triangle, the height may fall outside the triangle. You can extend the base and drop a perpendicular from the opposite vertex to this extension to find the height.
Why is the area of a triangle half the area of a related parallelogram?
A triangle is half of a parallelogram with the same base and height. If you duplicate a triangle and flip it, the two pieces fit together to form a parallelogram, so each triangle has half the parallelogram area.
What is Big Ideas Math Advanced 2 Chapter 13 about?
Chapter 13 covers Circles and Area, including circle area and circumference, areas of triangles, quadrilaterals, and composite figures.