Point P is in the interior of triangle ABC, and the lines through P are parallel to the sides of ABC. The three triangles shown in the diagram have areas of 4, 9, and 49. What is the area of triangle ABC?
144
DE is parallel to AC FG is parallel to BC IH is parallel to AB △PIE=49, △PDF=4, △PGH=9 △PGH≅△PIE HP:PI= sqrt(9) : sqrt(49)=3:7 --> IP:IH=7:10 --> △PIE:△HIC=7 ^2 :10^2 --> area of △HIC=100 area of parallelogram PGCE=100−9−49=42 similarly, area of parallelogram PIBF=28 and area of parallelogram PDAH=12 so area of △ABC=49+4+9+28+42+12=144
Assume triangle ABC can be divided into 6 smaller triangles, as shown below, with the areas given. What is the area of the entire triangle ABC?
Point P is in the interior of the equilateral triangle ABC. If AP = 7, BP = 5, and CP = 6, what is the area of ABC?
A circle contains triangle ABC. For each side, construct the perpendicular bisector and extend it to the exterior of the triangle to the circle. The three such lengths are 1, 2, 3, as shown.
What is the area of triangle ABC?
Three unit squares and two lines are shown. What is the area of triangle ABC?
