Half base times height.
Basic formula when base and perpendicular height are known.
Direct
AI Solver by AskSia
Triangle Area Solver: the right formula each time
Type or photograph the known triangle data. AskSia picks the right formula: (1/2)*base*height for SSA, Heron's formula for SSS, (1/2)*ab*sin(C) for SAS, or coordinate cross-product for vertex coordinates.
Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
4.9 / 5 · trusted by 2M+ students · 50M+ problems solved
asksia.ai/solver
98% · Verified
Problem
Find the area enclosed between y = x² and y = 2x in the first quadrant.
1
Find the points of intersection
Set the curves equal: x² = 2x → x(x - 2) = 0, so x = 0 and x = 2.
2
Identify which curve is on top
On (0, 2), 2x > x², so y = 2x is the upper curve.
3
Set up the area integral
A = ∫₀² (2x - x²) dx
4
Integrate term-by-term
A = [ x² - x³/3 ]₀²
Final Answer
A = 4/3 sq. units
Quick Answer
How do you find the area of a triangle?
Several formulas work depending on what you know. The basic formula is A = (1/2)*base*height, where height is the perpendicular distance from the base to the opposite vertex. If you know two sides and the included angle, A = (1/2)*a*b*sin(C). If you know all three sides, use Heron's formula: A = sqrt(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2 is the semi-perimeter. If you know the coordinates of all three vertices, use the cross-product or determinant formula.
98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Why students use AskSia for Triangle Area.
Every step transparent, every answer self-checked.
Two sides and angle.
(1/2)*a*b*sin(C). AskSia computes sin(C) and multiplies.
SAS
Heron's formula.
Three sides given. Compute semi-perimeter s, then sqrt(s(s-a)(s-b)(s-c)).
SSS
Coordinate formula.
Three vertices. Use (1/2)|x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|.
Coordinates
Photo, paste, or type.
Snap handwritten or printed problems with your phone, paste from any online homework portal, or type with full LaTeX support.
Multi-modal input
Verified by AskSia.
Every answer gets a self-check pass. Sia catches sign errors and algebra mistakes before you submit your homework.
Self-checked
How It Works
Solve any Triangle Area problem in three steps.
Step 01
Enter the problem.
Type the expression, paste from your homework, snap a photo, or speak it. AskSia parses your input and identifies the structure.
Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02
AskSia picks the method.
Based on the problem structure, AskSia chooses the cleanest solution path and labels each step with the operation performed.
1
Set curves equal
x² = 2x → x = 0, x = 2
2
Set up the integral
A = ∫₀² (2x - x²) dx
3
Evaluate
A = [x² - x³/3]₀² = 4/3
Step 03
Read the verified answer.
Final result appears with a substitution or composition check. Practice problems on the same concept are one tap away.
Auto-generated diagram
Region between y = 2x and y = x² — area = 4/3
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Split-panel interface with the worked solution on the left, the auto-generated diagram and AI tutor chat on the right.
Drag & drop image upload + LaTeX equation editor
Auto-generated diagrams render alongside steps
Side-panel AI tutor chat for hints and alt methods
Export to PDF, DOCX, Notion, or Google Docs
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Calculus
98% verified
1.4s
Step 4 of 4 · Evaluate
A = [x² - x³/3]₀² = 4/3
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98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
What the Triangle Area solver covers.
Base and height.
Right and oblique triangles with base and perpendicular height.
Basic
Two sides, included angle.
(1/2)*ab*sin(C). Common in SAS problems.
SAS
All three sides.
Heron's formula. Compute s, then the radical.
SSS
Three vertices.
Coordinate cross-product. Always positive (use absolute value).
Coordinates
Word problems.
Land plots, signage, triangular regions in real-world contexts.
Applied
Verify your homework.
Paste your candidate answer and the original problem. AskSia walks the work, flags any divergent step, and tells you the correct final value.
Answer check
Compare
AskSia vs. ChatGPT,
Photomath & Symbolab.
General chatbots hallucinate. Photo solvers stop at math. AskSia is built for actual coursework with verified accuracy, visual learning, and every subject.
| Feature | AskSia Solver | ChatGPT | Photo Solvers |
|---|---|---|---|
| Solution accuracy | ✓ 98% | ~70-85%, hallucinations | ~90%, math only |
| Auto-generated diagrams | ✓ Every solve | Inconsistent / broken | Graphs only, math-only |
| Step-by-step explanations | ✓ Numbered + plain English | Inconsistent depth | ✓ Math steps |
| Subject coverage | ✓ Math, Physics, Chem, Bio, CS, Econ | ✓ Wide but unverified | Math only |
| Photo input | ✓ Handwriting + diagrams + code | Photos OK, weak on handwriting | ✓ Math photos only |
| Answer verification | ✓ Self-checked before display | No verification | Math engine only |
| Tutor follow-ups | ✓ Hints, alt methods, ELI5 | ✓ General chat | Not available |
| Practice and flashcards | ✓ One-tap from any solve | Manual prompting | Not available |
| Code debugging | ✓ Python, Java, C++, SQL... | ✓ Yes | Not available |
| Free to start | ✓ Daily solves, no card | Limited model access | Steps locked behind paywall |
FAQ
Frequently asked questions.
Why is the area half base times height?
Because a triangle is half of a parallelogram with the same base and height. Take any triangle, duplicate it (rotated 180 degrees), and join along one side; the result is a parallelogram of area base * height. So the triangle is half of that, giving area = (1/2) * base * height. The height must be the perpendicular distance from the base to the opposite vertex.
How does Heron's formula work?
Heron's formula gives the area when you know all three sides a, b, c. Compute the semi-perimeter s = (a+b+c)/2, then the area is sqrt(s(s-a)(s-b)(s-c)). It works for any triangle, including obtuse and right triangles. The proof uses the law of cosines to express sin(C) in terms of the sides and then substitutes into (1/2)*ab*sin(C).
What is the coordinate formula for triangle area?
For vertices (x1, y1), (x2, y2), (x3, y3), the area is (1/2)|x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|. This comes from the cross-product of two edge vectors. The absolute value ensures the area is positive regardless of the order of vertices. AskSia uses this formula when you provide vertex coordinates.
When should I use SAS versus Heron's?
Use (1/2)*ab*sin(C) when you know two sides and the included angle (the angle between them). Use Heron's when you know all three sides but no angles. If you have two sides and a non-included angle (SSA), first use the law of sines to find the third side or another angle, then apply the appropriate formula. AskSia picks the right tool based on what you provide.
How accurate is AskSia?
AskSia is engineered for accuracy on standard high school and college coursework. Accuracy comes from subject-specialized models, a symbolic verification pass that catches arithmetic errors, and a self-check step that re-derives the answer before showing it to you.
Can I get practice problems and flashcards?
Yes. After any solve, ask Sia to generate similar practice problems at SAT, ACT, AP, IB, or college difficulty, or build a flashcard set on the underlying concept in one tap. Useful for exam prep and spaced repetition before a quiz, midterm, or final.
How much does AskSia cost?
AskSia has a free plan that includes daily solves across all subjects. AskSia Pro and Super include unlimited solves, advanced subjects, the full AI tutor companion, exports, and priority response speed. See pricing for details.
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Base-height, SAS, Heron, coordinates.
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