Take note Theorem 10-8: Area of a Triangle Given SAS

The area of a triangle is half the product of the lengths of two sides and the sine of the included angle.

Area of Δ A B C = 1 2 b c ( sin   A ) cap delta eh b c , equals . 1 half , b c open sine eh close

Problem 3 Finding Area

What is the area of the triangle?

Area = 1 2   ·  side length  ·  side length  ·  sine of included angle = 1 2 · 1 2 · 21 · sin 48 ° Substitute . ≈ 93   .63624801 Use a calculator . table with 2 rows and 1 column , row1 column 1 , cap area , equals , 1 half , middle dot . sidelength . middle dot . sidelength . middle dot . sineofincludedangle , row2 column 1 , table with 2 rows and 2 columns , row1 column 1 , equals , 1 half , middle dot , 1 half , middle dot 21 middle dot sine , 48 degrees , column 2 cap substitute . . , row2 column 1 , almost equal to 93 . .63624801 , column 2 cap useacalculator . . , end table , end table

The area of the triangle is about 94   cm 2 . 94 , cm squared , .

✓ Got It?

3. What is the area of the triangle? Round your answer to the nearest square inch.