SAT · Super Challenge
Find the area of a triangle that is not a right triangle. Box the triangle in a rectangle, then subtract the corner right triangles.
Inscribe the triangle in a rectangle. Subtract the three right triangles in the corners.
A triangle has vertices A(2, 1), B(8, 3), and C(5, 7). Find the area.
Draw a rectangle around the triangle. Each side of the rectangle passes through the highest, lowest, leftmost, or rightmost vertex.
The width is 8 − 2 = 6.
The height is 7 − 1 = 6.
A = ℓw
A = 6 × 6
A = 36
Three right triangles fill the corners. Find each area.
Right angle at (8, 1). The legs are 6 and 2.
A = 12bh
A = 12 × 6 × 2
A = 6
Right angle at (8, 7). The legs are 3 and 4.
A = 12bh
A = 12 × 3 × 4
A = 6
Right angle at (2, 7). The legs are 3 and 6.
A = 12bh
A = 12 × 3 × 6
A = 9
Area of the triangle = area of the rectangle − the three right triangles.
36 − 6 − 6 − 9 = 15
Answer: 15
A triangle has vertices A(1, 4), B(7, 2), and C(3, 8). Find the area.
Draw a rectangle around the triangle. Each side of the rectangle passes through the highest, lowest, leftmost, or rightmost vertex.
The width is 7 − 1 = 6.
The height is 8 − 2 = 6.
A = ℓw
A = 6 × 6
A = 36
Three right triangles fill the corners. Find each area.
Right angle at (1, 2). The legs are 6 and 2.
A = 12bh
A = 12 × 6 × 2
A = 6
Right angle at (7, 8). The legs are 4 and 6.
A = 12bh
A = 12 × 4 × 6
A = 12
Right angle at (1, 8). The legs are 2 and 4.
A = 12bh
A = 12 × 2 × 4
A = 4
Area of the triangle = area of the rectangle − the three right triangles.
36 − 6 − 12 − 4 = 14
Answer: 14
A triangle has vertices A(2, 7), B(9, 5), and C(4, 1). Find the area.
Draw a rectangle around the triangle. Each side of the rectangle passes through the highest, lowest, leftmost, or rightmost vertex.
The width is 9 − 2 = 7.
The height is 7 − 1 = 6.
A = ℓw
A = 7 × 6
A = 42
Three right triangles fill the corners. Find each area.
Right angle at (9, 7). The legs are 7 and 2.
A = 12bh
A = 12 × 7 × 2
A = 7
Right angle at (9, 1). The legs are 5 and 4.
A = 12bh
A = 12 × 5 × 4
A = 10
Right angle at (2, 1). The legs are 2 and 6.
A = 12bh
A = 12 × 2 × 6
A = 6
Area of the triangle = area of the rectangle − the three right triangles.
42 − 7 − 10 − 6 = 19
Answer: 19
A triangle has vertices A(9, 8), B(1, 5), and C(5, 2). Find the area.
Draw a rectangle around the triangle. Each side of the rectangle passes through the highest, lowest, leftmost, or rightmost vertex.
The width is 9 − 1 = 8.
The height is 8 − 2 = 6.
A = ℓw
A = 8 × 6
A = 48
Three right triangles fill the corners. Find each area.
Right angle at (1, 8). The legs are 8 and 3.
A = 12bh
A = 12 × 8 × 3
A = 12
Right angle at (1, 2). The legs are 4 and 3.
A = 12bh
A = 12 × 4 × 3
A = 6
Right angle at (9, 2). The legs are 4 and 6.
A = 12bh
A = 12 × 4 × 6
A = 12
Area of the triangle = area of the rectangle − the three right triangles.
48 − 12 − 6 − 12 = 18
Answer: 18
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