Let’s solve each triangle one by one. Remember, the area of a triangle is:
Area = (base × height) ÷ 2
We need to pick the correct base and height — they must be perpendicular to each other (that’s what the little square symbol means).
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First Triangle:
It has two parts on the bottom: 3 ft and 12 ft. So total base = 3 + 12 =
15 ft
The height is given as
7 ft (the dashed line with the right angle mark).
So,
Area = (15 × 7) ÷ 2
= 105 ÷ 2
=
52.5 ft²
Wait — let me double-check. The diagram shows the height dropping down to the point between the 3 ft and 12 ft segments. That means the full base is indeed 3 + 12 = 15 ft, and the height is 7 ft. Yes, that’s correct.
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Second Triangle:
This one is tricky. It’s not drawn with a horizontal base. But we see a side labeled
9 in. and a dashed line from the opposite vertex meeting it at a right angle, labeled
18 in.
That means:
→ Base = 9 in.
→ Height = 18 in.
Even though the triangle looks slanted, as long as the height is perpendicular to the base, we can use them.
Area = (9 × 18) ÷ 2
= 162 ÷ 2
=
81 in²
Note: The other sides (32 in. and 36 in.) are distractors — we don’t need them because we already have a base and its corresponding height.
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Third Triangle:
Top side is split into 8 m and 16 m → total base = 8 + 16 =
24 m
Height is the dashed line going down:
14 m
Area = (24 × 14) ÷ 2
First, 24 × 14:
20 × 14 = 280
4 × 14 = 56
Total = 280 + 56 = 336
Then divide by 2: 336 ÷ 2 =
168 m²
Again, the 16 m on the left side is not needed — it’s just part of the shape, but not the base for this height.
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Final Answer:
First triangle: 52.5 ft²
Second triangle: 81 in²
Third triangle: 168 m²
Parent Tip: Review the logic above to help your child master the concept of area of triangle worksheet.
