Average base times height.
(b1 + b2)/2 is the average base. Times h gives the area.
Formula
AI Solver by AskSia
Area of a Trapezoid Solver: the formula and the answer
Type or photograph the two parallel sides and the height. AskSia applies A = (1/2)(b1 + b2)*h with values plugged in. Both rectangular- and isosceles-trapezoid problems handled.
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
What is the formula for the area of a trapezoid?
A trapezoid is a quadrilateral with exactly one pair of parallel sides (in American usage). Its area equals half the sum of the parallel sides times the perpendicular height between them: A = (1/2)*(b1 + b2)*h, where b1 and b2 are the lengths of the two parallel sides (the 'bases') and h is the perpendicular distance between them. This formula works for any trapezoid, including isosceles and right trapezoids.
98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Why students use AskSia for Area of a Trapezoid.
Every step transparent, every answer self-checked.
Height is perpendicular.
h is the perpendicular distance between the parallel sides, not a slanted side.
Precision
Right and isosceles cases.
Right trapezoid has one perpendicular side. Isosceles has equal non-parallel sides.
Types
Decompose to triangle and rectangle.
On request, AskSia shows the formula derived by splitting into a rectangle plus two triangles.
Concept
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 Area of a Trapezoid 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
Available On
Solve anywhere
you study.
Every solve syncs across Web, iOS, and Android — start it at your desk, finish on your phone.
Web App
Full study studio
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
Hi! What are we studying today?
Ask about your homework, lecture, or readings...↑
Calculus
98% verified
1.4s
Step 4 of 4 · Evaluate
A = [x² - x³/3]₀² = 4/3
Mobile App
Snap & solve, anywhere
Open the camera, frame the problem, and the worked solution plus diagram appear in seconds.
One-tap snap-and-solve on iOS and Android
Pinch-to-zoom diagrams, swipe between steps
Auto-sync solves with your Web library
Offline review of saved solutions and flashcards
☰
AskSia
+What can I do for you?
Homework solver
Live transcribe
File summary
Snap
YouTube
Flashcard
Calc
98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
What the Area of a Trapezoid solver covers.
Standard trapezoid.
b1, b2, h all known. Direct formula application.
Direct
Right trapezoid.
One non-parallel side is perpendicular. h equals that side.
Right
Isosceles trapezoid.
Non-parallel sides are equal. h found using Pythagorean theorem.
Isosceles
Composite figures.
Trapezoid plus other shapes. AskSia decomposes.
Composite
Real-world.
Land plots, sail panels, signage with trapezoidal shape.
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 formula half the sum of the bases times the height?
Because the average of the two bases gives a 'representative width,' and multiplying by the height gives the area. You can see this by splitting the trapezoid along a diagonal into two triangles: each has area (1/2)*base*height, and adding gives (1/2)*(b1*h + b2*h) = (1/2)*(b1+b2)*h.
What if the height is not given directly?
For an isosceles trapezoid, the height can be found using the Pythagorean theorem applied to the slanted non-parallel side and the horizontal offset (half the difference of bases). AskSia performs this Pythagorean step explicitly if you provide the non-parallel side length instead of the height.
Is a parallelogram a trapezoid?
It depends on the definition. In American math, a trapezoid has exactly one pair of parallel sides, so a parallelogram is not a trapezoid. In British math (and some inclusive definitions), a trapezoid has at least one pair of parallel sides, which includes parallelograms. AskSia uses the American convention by default.
Can a trapezoid be concave?
A standard trapezoid is convex by definition (all interior angles less than 180 degrees). Concave four-sided figures with one pair of parallel sides are still sometimes called trapezoids in some contexts, but the area formula needs careful adjustment using signed lengths. AskSia handles convex trapezoids by default.
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.
Start Today
Half the base sum, times the height.
Join 2M+ students using AskSia to solve area of a trapezoid problems step-by-step. Photo input, plain-English explanations, and a verification check on every solve.
Let's Get in Touch
