SOLUTION: Please help me solve this question: ABCD is a square with 8 inch sides. Point E is the midpoint of side AB and point F is the midpoint of side BC. What is the area of the triangle

Algebra ->  Permutations -> SOLUTION: Please help me solve this question: ABCD is a square with 8 inch sides. Point E is the midpoint of side AB and point F is the midpoint of side BC. What is the area of the triangle       Log On


   

Question 959238: Please help me solve this question: ABCD is a square with 8 inch sides. Point E is the midpoint of side AB and point F is the midpoint of side BC. What is the area of the triangle DEF?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Triangles AED and CDF are right triangles with legs 4 in and 8 in,
so each has area (1/2)(4in)(8in)=16 square inches.
The small triangle EBF is a isosceles right triangle with legs 4 inches,
so has an area of (1/2)(4in)(4in)=8 square inches.
The total area of the square is (8in)(8in)=64 square inches.
The area of square square ABCD is the sum of the four triangles,
so the area of triangle DEF = Area ABCD - Area AED - Area CDF - Area EBF
Area DEF=64in%5E2-16in%5E2-16in%5E2-8in%5E2=64in%5E2-40in%5E2=24in%5E2
ANSWER: The area of triangle DEF is 24 square inches.