The area of the triangle DEF is approximately equal to 144.014 square units.
How to find the area of a triangle by Heron's formula
Triangles can be generated on a Cartesian plane by marking three non-colinear points on there. Heron's formula offers the possibility of calculating the area of a triangle by only using the lengths of its three sides, whose formula is now introduced:
A = √ [s · (s - DE) · (s - EF) · (s - DF)] (1)
s = (DE + EF + DF) / 2 (2)
Where s is the semiperimeter of the triangle.
First, we determine the lengths of the sides DE, EF and DF by Pythagorean theorem:
Side DE
DE = √ [[10 - (- 8)]² + (- 2 - 8)²]
DE ≈ 20.591
Side EF
EF = √ [(- 8 - 10)² + [- 8 - (- 2)]²]
EF ≈ 18.974
Side DF
DF = √[[- 8 - (- 8)]² + (- 8 - 8)²]
DF = 16
Then, the area of the triangle DEF is by Heron's formula:
s = (16 + 18.974 + 20.591) / 2
s = 27.783
A = √[27.783 · (27.783 - 20.591) · (27.783 - 18.974) · (27.783 - 16)]
A ≈ 144.014
The area of the triangle DEF is approximately equal to 144.014 square units.
To learn more on Heron's formula: https://brainly.com/question/15188806
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