Grade 10 · Compare a triangle's base and altitude · 416 of 750
Compare a triangle's base and altitude · practice 43
Find the area of a triangle with base 1 and perpendicular height 9.5. Follow the calculation, then test the quantities in the animated example.
Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.
01 · Make a prediction
Your practice question
Find the area of a triangle with base 1 and perpendicular height 9.5.
Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.
A starting point
Compare with the rectangle having the same base and perpendicular height.
Work through the reasoning
Step 1
Translate the givens
The base is 1 length units and the perpendicular height is 9.5; a slanted edge cannot replace that height.
Step 2
Calculate with the model
The matching rectangle has area 1 × 9.5 = 9.5. A triangle occupies half, so 9.5 ÷ 2 = 4.75.
Step 3
Check and interpret
Twice the triangle's area is 2 × 4.75 = 9.5, matching the rectangle. Area is measured in square units.
The answer
4.75 square units.
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
02 · Explore the model
See the mathematical relationship move.
Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.
Watch the relationship
PausedHD animation studio
From experiment to screen.
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The mathematical idea
A triangle with a horizontal base occupies half of the rectangle sharing that base and perpendicular height. Pairing it with a congruent triangle explains the factor one half. Slanted edge length cannot replace perpendicular height in the formula. Starting quantities: Base length = 1; Perpendicular height = 9.5.
A = base × perpendicular height / 2
03 · Reflect and transfer
Explain what changes and why.
What happens to the area if only the perpendicular height doubles?
This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.