Area of Triangles Worksheets | PYP IB Grade 5 - Free Printable

Let’s solve each triangle area problem step by step using the formula:

Area = ½ × base × height

We must always use the base and the height that is perpendicular to it (the dotted or marked line showing the true height).

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Triangle b:

- Base = 6 cm (bottom side)
- Height = 8 cm (dotted line from top vertex down to base — this is perpendicular, even though it falls outside the triangle)
→ Area = ½ × 6 × 8 = 3 × 8 = 24 sq cm

*(Note: The 10 cm side is the hypotenuse — we don’t use it for area calculation here.)*

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Triangle c:

- Base = 8 cm (side labeled at bottom right)
- Height = 9 cm (dotted line drawn perpendicular to that base)
→ Area = ½ × 8 × 9 = 4 × 9 = 36 sq cm

*(The two 10 cm sides are equal — it’s an isosceles triangle — but again, we only care about the given base and its matching height.)*

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Triangle d:

- Base = 10 cm (bottom side)
- Height = 6 cm (line drawn from top vertex to base — looks like it hits the base perpendicularly? Wait — actually, looking carefully: the height is drawn to one of the 10 cm sides, not the bottom. But in the diagram, the height “h = 6 cm” is shown going to the side labeled 10 cm on the left. So we should take that 10 cm as the base.

Actually, let’s recheck: In triangle d, all three sides are 10 cm — it’s equilateral. The height h=6 cm is drawn from the top vertex to the left side (which is 10 cm). So if we take that 10 cm side as the base, then height is 6 cm.

→ Area = ½ × 10 × 6 = 5 × 6 = 30 sq cm

*(Even though it’s equilateral, we’re told the height to one side is 6 cm — so we use that.)*

Wait — but in reality, for an equilateral triangle with side 10 cm, the actual height would be √(10² - 5²) = √75 ≈ 8.66 cm. But since the worksheet says h = 6 cm, we go with what’s given — maybe it’s not drawn to scale or it’s a different configuration. We follow the diagram’s labels.

So yes — base = 10 cm, height = 6 cm → Area = 30 sq cm.

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Triangle e:

- Base = 6 cm (bottom side)
- Height = 7 cm (dotted line from top vertex straight down to base — perpendicular)
→ Area = ½ × 6 × 7 = 3 × 7 = 21 sq cm

*(The other sides — 9 cm and 6 cm — are just extra info; we ignore them for area.)*

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Triangle f:

- Base = 6 cm (bottom side)
- Height = 6 cm (dotted line from top vertex down to base — perpendicular)
→ Area = ½ × 6 × 6 = 3 × 6 = 18 sq cm

*(Again, the 5 cm and 7 cm sides are not needed — we use the base and its corresponding height.)*

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Now let’s list all answers clearly:

b. 24 sq cm
c. 36 sq cm
d. 30 sq cm
e. 21 sq cm
f. 18 sq cm

Double-checking calculations:

b: ½×6×8 = 24 ✔️
c: ½×8×9 = 36 ✔️
d: ½×10×6 = 30 ✔️
e: ½×6×7 = 21 ✔️
f: ½×6×6 = 18 ✔️

All correct.

Final Answer:
b. 24 sq cm
c. 36 sq cm
d. 30 sq cm
e. 21 sq cm
f. 18 sq cm