The area of ΔEFG is 8.9 square centimeter.
The area of a SAS triangle is the total amount of space it encloses in a 2-dimensional plane. "SAS" which means "Side, Angle, Side", is the property of a triangle whose 2 sides and the angle between these sides is given.
The formula to calculate the area of a triangle using SAS is given as,
1. When sides 'b' and 'c' and included angle A is known, the area of the triangle is: 1/2 × bc × sin(A)
2. When sides 'b' and 'a' and included angle B is known, the area of the triangle is: 1/2 × ab × sin(C)
3. When sides 'a' and 'c' and included angle C is known, the area of the triangle is: 1/2 × ac × sin(B)
Given
In ΔEFG
g = 5.2 cm
e = 5.1 cm
∠F=42°.
Area of SAS triangle = [tex]\frac{1}{2} absinC[/tex]
Area = [tex]\frac{1}{2} (5.2)(5.1)sin42^{0}[/tex]
Area = 8.873 ≅ 8.9 (nearest tenth)
Hence, the area of ΔEFG is 8.9 square centimeter.
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