How to Find the Area of a Trapezium with No Parallel Sides

Step-by-Step Guide

1. 1

   Step 1: Break down the trapezium into two triangles.

   Label your triangles as triangle A and triangle B.
   
   Look at the picture for help.(The image does not scale.) , (Example values are below their pictures) Triangle A: a{\displaystyle a}=70, b{\displaystyle b}=13, and c{\displaystyle c}=15.
   
   Triangle B: a{\displaystyle a}=91, b{\displaystyle b}=11, and c{\displaystyle c}=9. , Plug the values from the second step in the formula.
   
   Triangle A:
   A=bc/2(sin∗a)=(13)(15)/2(sin70)≈45.8101{\displaystyle A=bc/2(sin*a)=(13)(15)/2(sin70)\approx
   45.8101} Triangle B:
   A=bc/2(sin∗a)=(11)(9)/2(sin91)≈49.4901{\displaystyle A=bc/2(sin*a)=(11)(9)/2(sin91)\approx
   49.4901} , That is your final answer!
   45.8101+49.4901=95.7102.A≈95.7102{\displaystyle
   45.8101+49.4901=95.7102.A\approx
   95.7102}
2. 2

   Step 2: Find the values for a{\displaystyle a}

3. 3

   Step 3: b{\displaystyle b}

4. 4

   Step 4: and c{\displaystyle c} for both triangles A and B where a{\displaystyle a}= the included angle of the sides a{\displaystyle a} and b{\displaystyle b}

5. 5

   Step 5: b{\displaystyle b}= one of the two sides that you know

6. 6

   Step 6: and c{\displaystyle c}= the other side that you know.

7. 7

   Step 7: Use the formula A=bc/2(sin∗a){\displaystyle A=bc/2(sin*a)} to calculate the areas of the triangles.

8. 8

   Step 8: Add the areas for the triangles A and B.

Detailed Guide

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