Area of Triangles

Calculating the area of a triangle depends on the kind of triangle you have.

Get started Sign up for free
Area of Triangles Area of Triangles

Create learning materials about Area of Triangles with our free learning app!

  • Instand access to millions of learning materials
  • Flashcards, notes, mock-exams and more
  • Everything you need to ace your exams
Create a free account

Convert documents into flashcards for free with AI!

Contents
Table of contents

    Formulas for calculating the area of a triangle

    The area of a triangle can be found in two formulas:

    • For all triangles, you can use the formula: area=base×height2

    Area of triangles Showing a triangle's base and height StudySmarterShowing a triangle's base and height - StudySmarter Originals

    Triangle A is shown below (all lengths are in cm):

    Area of triangles Worked example of area of a triangle StudySmarter

    • The area of the triangle = 10×52 = 25 cm2

    For most triangles, the base and height are used as shown above.

    • For all non-angled triangles, the formula is area=a×b×sin(c)2

    Area of triangles a non angled triangle StudySmarterA non-angled triangle - StudySmarter Orignals

    To use this formula, angle C needs to be between the two sides. You can remember this through the acronym SAS (Side, Angle, Side).

    A triangle is shown below (all lengths are in cm)

    Area of triangles Worked example for finding area of a triangle StudySmarter

    What is the area of the triangle?

    • First, label the sides of the triangles according to the formula.
    • This is not a right-angled triangle. We can use the formula below.
    • Area of the triangle = a×b×sinc2=12×28×sin4002=107.99 cm2

    Right-angled triangles

    For right-angled triangles, the height for the right-angled triangle in the formula area=base×height2is equivalent to the vertical side.

    Area of triangles Showing the base and height of a right angle triangle StudySmarterA right angle triangle

    • When using the formula you might need to work out one of the sides to get two sides next to the angle. To do so, you need to use Pythagoras theorem, wherebya2+b2=c2

    Area of triangles Showing the sides of a right angle triangle StudySmarter

    An equilateral triangle can be seen below (all lengths are in cm):

    Area of triangles Worked example for finding area of a triangle StudySmarter

    The formula for the area of the triangle is base x height2 but the height is unknown. To work out the height, you need to rearrange and use Pythagoras theorem.

    1. To use Pythagoras theorem, you need to find a and c: c is the hypotenuse and therefore, c = 5; a is half the base and therefore a = 4.
    2. Substitute the values into Pythagoras theorem: c2-a2 = 25-16=9=3. Therefore, the height is 3.
    3. Substitute the values into the Area of a Triangle formula: b×h2=8×32=12 cm2

    Area of Triangles - Key takeaways

    • The area of any triangle can be calculated using the formula Area=base×height2
    • For all non-right-angled triangles, you can also use the formula Area=12×a×b×Sin(C)
    • The acronym SAS is used to figure out what values should be substituted into Area=12×a×b×sin(C)
    Area of Triangles Area of Triangles
    Learn with 1 Area of Triangles flashcards in the free StudySmarter app

    We have 14,000 flashcards about Dynamic Landscapes.

    Sign up with Email

    Already have an account? Log in

    Frequently Asked Questions about Area of Triangles

    What is the area of a triangle?

    The area of the triangle is the amount of space that the triangle takes up.

    How do you work out the area of the triangle?

    The area of any triangle can be found using the formula, area=1/2(absin(c)) or you can also use the formula area= (base ×  height)/2 if the triangle is right-angled.

    How do you measure the area of the triangle?

    The unit of the triangle’s area is the unit the side is measured in ^2 so if the sides were measured in metres the unit of the area would be m^2.

    Discover learning materials with the free StudySmarter app

    Sign up for free
    1
    About StudySmarter

    StudySmarter is a globally recognized educational technology company, offering a holistic learning platform designed for students of all ages and educational levels. Our platform provides learning support for a wide range of subjects, including STEM, Social Sciences, and Languages and also helps students to successfully master various tests and exams worldwide, such as GCSE, A Level, SAT, ACT, Abitur, and more. We offer an extensive library of learning materials, including interactive flashcards, comprehensive textbook solutions, and detailed explanations. The cutting-edge technology and tools we provide help students create their own learning materials. StudySmarter’s content is not only expert-verified but also regularly updated to ensure accuracy and relevance.

    Learn more
    StudySmarter Editorial Team

    Team Math Teachers

    • 3 minutes reading time
    • Checked by StudySmarter Editorial Team
    Save Explanation Save Explanation

    Study anywhere. Anytime.Across all devices.

    Sign-up for free

    Sign up to highlight and take notes. It’s 100% free.

    Join over 22 million students in learning with our StudySmarter App

    The first learning app that truly has everything you need to ace your exams in one place

    • Flashcards & Quizzes
    • AI Study Assistant
    • Study Planner
    • Mock-Exams
    • Smart Note-Taking
    Join over 22 million students in learning with our StudySmarter App
    Sign up with Email

    Get unlimited access with a free StudySmarter account.

    • Instant access to millions of learning materials.
    • Flashcards, notes, mock-exams, AI tools and more.
    • Everything you need to ace your exams.
    Second Popup Banner