Let’s solve each triangle one by one.
We’ll use the formula for area of a triangle:
Area = (base × height) ÷ 2
But note — in some triangles, we’re given all three sides and a height drawn to one side. In those cases, we can pick any side as the base, but we must use the height that goes perpendicular to that base.
Looking at the diagrams:
---
Triangle 1:
It’s an equilateral triangle with all sides = 9.
The height is labeled as
7.794, and it’s drawn from the top vertex down to the bottom side (which is also 9).
So we can use base = 9, height = 7.794
→ Area = (9 × 7.794) ÷ 2
= 70.146 ÷ 2
=
35.073
---
Triangle 2:
Right triangle? Looks like it — legs are 7 and 15, hypotenuse 16.48.
In right triangles, the two legs are perpendicular → so we can use them as base and height.
→ Area = (15 × 7) ÷ 2
= 105 ÷ 2
=
52.5
*(Note: We don’t need the hypotenuse for area if we have the two legs.)*
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Triangle 3:
Equilateral triangle again — all sides = 3. Height = 2.598 (drawn to base of 3)
→ Area = (3 × 2.598) ÷ 2
= 7.794 ÷ 2
=
3.897
---
Triangle 4:
Right triangle? Legs appear to be 5 and 14, hypotenuse 14.69.
Again, use the two legs as base and height.
→ Area = (14 × 5) ÷ 2
= 70 ÷ 2
=
35
---
Triangle 5:
Scalene triangle — sides 13, 7, 15. Height = 6.00 is drawn to the side of length 15.
So base = 15, height = 6.00
→ Area = (15 × 6) ÷ 2
= 90 ÷ 2
=
45
---
Triangle 6:
Isosceles triangle — two sides = 4, base = 4? Wait — actually, looking closely:
All sides are labeled 4? But height is 3.46 drawn to the base of 4.
Wait — if all sides are 4, it’s equilateral. But height should be about 3.464 for side 4 — yes, matches.
So base = 4, height = 3.46
→ Area = (4 × 3.46) ÷ 2
= 13.84 ÷ 2
=
6.92
*(Note: If you use more precise height √(4² - 2²) = √12 ≈ 3.464, then area = (4×3.464)/2 = 6.928 — but since diagram says 3.46, we’ll use that.)*
---
Now let’s double-check each calculation quickly:
1. 9 × 7.794 = 70.146 → ÷2 = 35.073
✔
2. 15 × 7 = 105 → ÷2 = 52.5
✔
3. 3 × 2.598 = 7.794 → ÷2 = 3.897
✔
4. 14 × 5 = 70 → ÷2 = 35
✔
5. 15 × 6 = 90 → ÷2 = 45
✔
6. 4 × 3.46 = 13.84 → ÷2 = 6.92
✔
All correct.
Final Answer:
1. 35.073
2. 52.5
3. 3.897
4. 35
5. 45
6. 6.92
Parent Tip: Review the logic above to help your child master the concept of area of triangle worksheet 6th grade.
