Explore · triangle area
An obtuse triangle has a base extended past a vertex. The perpendicular outside height is 5 cm and the corresponding base is 12 cm. Find its area.
Singapore Math 5A · Independent learning
Area of a Triangle — Part 2
Learning target: Identify the perpendicular height when the altitude lies outside an obtuse triangle.
Begin with the exact prerequisite checkpoint below. Afterward, explain why your strategy works, not merely which procedure to use.
Opening task
Lesson-specific prerequisite checkpoint
Do this without a worked example. If you cannot explain it, review the earlier skill before continuing.
A triangle has a horizontal base. Which type of line measures its height?
Understand the idea
Identify the perpendicular height when the altitude lies outside an obtuse triangle.
For an obtuse triangle, the altitude from a vertex can fall on an extension of the opposite side. Extend the base, draw a perpendicular dashed line, and use its length as the height. The triangle area formula remains half base×perpendicular height.
Vocabulary focus: unit conversion, perpendicular height, square units. Make a small labeled model, work through the arithmetic, and explain the result in words.
Watch for: Assuming every altitude must appear inside the triangle.
Model to study: Extended base and dashed perpendicular altitude.
Worked examples
Worked examples 1 · triangle area
An obtuse triangle has a base extended past a vertex. The perpendicular outside height is 3 cm and the corresponding base is 5 cm. Find its area.
Solution: 15/2 cm²
Why: Use the perpendicular height, whether inside or outside. Triangle area = 1/2 × 5 × 3 = 15/2 cm². A sloping side is not the height.
Worked examples 2 · triangle area
An obtuse triangle has a base extended past a vertex. The perpendicular outside height is 9 cm and the corresponding base is 9 cm. Find its area.
Solution: 81/2 cm²
Why: Use the perpendicular height, whether inside or outside. Triangle area = 1/2 × 9 × 9 = 81/2 cm². A sloping side is not the height.
Worked examples 3 · triangle area
An obtuse triangle has a base extended past a vertex. The perpendicular outside height is 8 cm and the corresponding base is 14 cm. Find its area.
Solution: 56 cm²
Why: Use the perpendicular height, whether inside or outside. Triangle area = 1/2 × 14 × 8 = 56 cm². A sloping side is not the height.
Check understanding
Check understanding 1 · triangle area
An obtuse triangle has a base extended past a vertex. The perpendicular outside height is 11 cm and the corresponding base is 14 cm. Find its area.
Check understanding 2 · triangle area
An obtuse triangle has a base extended past a vertex. The perpendicular outside height is 11 cm and the corresponding base is 10 cm. Find its area.
Guided practice
Guided practice 1 · triangle area
An obtuse triangle has a base extended past a vertex. The perpendicular outside height is 3 cm and the corresponding base is 11 cm. Find its area.
Guided practice 2 · triangle area
An obtuse triangle has a base extended past a vertex. The perpendicular outside height is 4 cm and the corresponding base is 15 cm. Find its area.
Guided practice 3 · triangle area
An obtuse triangle has a base extended past a vertex. The perpendicular outside height is 3 cm and the corresponding base is 10 cm. Find its area.
Independent practice
Independent practice 1 · triangle area
An obtuse triangle has a base extended past a vertex. The perpendicular outside height is 9 cm and the corresponding base is 4 cm. Find its area.
Independent practice 2 · triangle area
An obtuse triangle has a base extended past a vertex. The perpendicular outside height is 3 cm and the corresponding base is 8 cm. Find its area.
Independent practice 3 · triangle area
An obtuse triangle has a base extended past a vertex. The perpendicular outside height is 8 cm and the corresponding base is 15 cm. Find its area.
Independent practice 4 · triangle area
An obtuse triangle has a base extended past a vertex. The perpendicular outside height is 7 cm and the corresponding base is 11 cm. Find its area.
Independent practice 5 · triangle area
An obtuse triangle has a base extended past a vertex. The perpendicular outside height is 3 cm and the corresponding base is 7 cm. Find its area.
Challenge and error analysis
Challenge and error analysis 1 · worked-error diagnosis
Error-analysis notebook: Learner notebook (LESSON): “Triangle area = 15 × 6 = 90 cm². I omitted the factor one half.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: An obtuse triangle has a base extended past a vertex. The perpendicular outside height is 6 cm and the corresponding base is 15 cm. Find its area.
Challenge and error analysis 2 · reasoning transfer
Reasoning and transfer: Solve, then explain a different way to check your answer (inverse operation, estimate, model, or units as appropriate). An obtuse triangle has a base extended past a vertex. The perpendicular outside height is 10 cm and the corresponding base is 7 cm. Find its area.
Exit check
Exit check 1 · triangle area
An obtuse triangle has a base extended past a vertex. The perpendicular outside height is 9 cm and the corresponding base is 15 cm. Find its area.
Exit check 2 · triangle area
An obtuse triangle has a base extended past a vertex. The perpendicular outside height is 5 cm and the corresponding base is 6 cm. Find its area.
Target for independent mastery: all exit-check problems correct plus a justified explanation. A tutor may reteach the concept if calculations are correct without meaningful reasoning.