Calculating the Area of Acute, Right, and Obtuse Triangles
Each area of triangles worksheet draws true-to-scale right, acute, and obtuse triangles with explicit 90-degree perpendicular altitude markers for Grades 5–7 (CCSS.MATH.CONTENT.6.G.A.1)—because slanted side lengths on obtuse triangles trap students who multiply a slanted edge instead of the perpendicular height h in A = ½ × b × h.
Across classroom assessments on triangles, two errors account for nearly every lost point: forgetting to halve the base-times-height product, and mistaking a slanted side length for the altitude of obtuse or acute triangles. Our vector diagrams mark the right-angle box where the dashed altitude meets the base line—including external altitudes on obtuse triangles—so learners visually separate perpendicular height from perimeter edges.
Once students master direct area calculation for triangles, Set C flips the formula to missing-dimension triangles: students double the given area first (2A) before dividing by the known base or height, reinforcing algebraic reasoning with triangles.
| Triangles Classification | Where Perpendicular Height (h) Lies | Worked Triangles Formula | Standard |
|---|---|---|---|
| Right Triangles | Vertical leg of triangles forms 90° angle with base | b = 8, h = 6 → ½ × 8 × 6 = 24 cm² | CCSS 6.G.A.1 |
| Acute Triangles | Internal dashed altitude dropped inside triangles | b = 10, h = 7 → ½ × 10 × 7 = 35 cm² | CCSS 6.G.A.1 |
| Obtuse Triangles | External altitude dropped to extended base of triangles | b = 9, h = 4 → ½ × 9 × 4 = 18 cm² | CCSS 6.G.A.1 |
| Missing Base / Height Triangles | Double triangles area first: h = (2 × A) ÷ b | A = 30, b = 12 → h = 60 ÷ 12 = 5 cm | CCSS 7.G.B.6 |
Area of Triangles Classroom FAQ
Why do students forget to divide by 2 when finding the area of triangles?
Students often apply the rectangle formula (b × h) by mistake. Every triangle is exactly half of a parallelogram or rectangle sharing the same base and perpendicular height, so the area formula must multiply ½ × base × height.
How do you measure the height of obtuse triangles?
For obtuse triangles, the perpendicular altitude falls outside the triangle by extending the horizontal base line with a dashed segment and dropping a 90-degree vertical height from the opposite apex.
How do you find a missing base or height when given the area of a triangle?
First multiply the given area by 2 (since A = ½bh means 2A = bh), then divide 2A by the known base or height to isolate the missing dimension.