Area And Perimeter Of Parallelograms And Triangles | How To Find ... - Free Printable

Let’s solve each problem step by step. We’ll use the correct area formulas for each shape and work carefully.

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Problem 1: Rectangle
- Formula: Area = length × width
- Given: 6 m (height) and 12 m (base)
- Calculation: 6 × 12 = 72
- Units: square meters → 72 m²

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Problem 2: Parallelogram
- Formula: Area = base × height
- Given: base = 14 ft, height = 4 ft (the dashed line is the height!)
- Note: The side labeled “6 ft” is not needed — it’s a slant side, not the height.
- Calculation: 14 × 4 = 56
- Units: square feet → 56 ft²

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Problem 3: Triangle
- Formula: Area = (base × height) ÷ 2
- Given: base = 6 in, height = 4 in (dashed line with right angle mark)
- Sides 5 in and 3 in are not needed — they’re just sides, not height or base for this formula.
- Calculation: (6 × 4) ÷ 2 = 24 ÷ 2 = 12
- Units: square inches → 12 in²

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Problem 4: Parallelogram ABCD
- Formula: Area = base × height
- Given: base = 6 inches, height = 7 inches
- Side = 9 inches is extra info — don’t use it!
- Calculation: 6 × 7 = 42
- Units: square inches → 42 in²

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Problem 5: Triangle QRS
- It says: RS and QR form a right angle → so those two sides are the legs of a right triangle.
- So we can treat them as base and height.
- RS = 4 ft, QR = 7 ft → these are perpendicular.
- Formula: Area = (base × height) ÷ 2
- Calculation: (4 × 7) ÷ 2 = 28 ÷ 2 = 14
- Units: square feet → 14 ft²

*(Note: QS = 10 ft is the hypotenuse — not needed for area.)*

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Problem 6: Rectangle GHIJ
- In a rectangle, opposite sides are equal.
- GH = 14, IJ = 30 → but wait! That doesn’t make sense unless we misread.
Actually, in rectangle GHIJ:
- GH and IJ are opposite sides → should be equal? But here GH=14, IJ=30? That can’t be.
Wait — maybe it's a typo? Or perhaps GH and IJ are adjacent?

Let’s think: In rectangle GHIJ, vertices go G-H-I-J-G.
So sides: GH, HI, IJ, JG.
Opposite sides: GH = IJ, and HI = JG.

But problem says: GH = 14, IJ = 30 → contradiction? Unless...

Ah! Maybe it’s saying GH = 14 and IJ = 30 meaning those are two different sides? But that would mean it’s not a rectangle? No — probably it’s a mistake in interpretation.

Wait — perhaps it means GH = 14 and IJ = 30, but since IJ is opposite to GH, they must be equal. So likely, it’s meant to say GH = 14 and HI = 30? Or maybe GH and IJ are adjacent?

Actually, let’s re-read: “Rectangle GHIJ has side GH=14 and side IJ=30”

In standard labeling, if it’s GHIJ, then GH and IJ are opposite. So they must be equal. But 14 ≠ 30 → impossible.

Unless... maybe it’s a typo and it meant GH = 14 and HI = 30? That would make sense — adjacent sides.

Because in many problems, they give you length and width.

I think it’s safe to assume that GH and IJ are meant to be adjacent sides — or perhaps it’s a mislabeling.

Alternatively, maybe “side GH=14 and side IJ=30” — but in rectangle, IJ is same as GH? No.

Wait — perhaps it’s GH = 14 and IJ = 30, but IJ is not opposite? Let’s draw mentally:

G ---- H
| |
J ---- I

Then GH is top, IJ is bottom → opposite → should be equal.

But 14 ≠ 30 → error?

Perhaps it’s GH = 14 and HI = 30? That would make sense.

Looking at common textbook problems, when they say “rectangle has sides A and B”, they mean length and width.

I think it’s a wording issue. Probably, they mean one side is 14 and the other is 30.

Because otherwise, it’s impossible.

So I’ll assume: dimensions are 14 and 30.

Area = 14 × 30 = 420

Units: no units given, but probably square units → 420

*(If strict, we’d question the problem, but for student level, likely intended as 14 and 30 as length and width.)*

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Problem 7: Find the length of rectangle
- Given: Area = 78 mm², width = 13 mm
- Formula: Area = length × width → so length = Area ÷ width
- Calculation: 78 ÷ 13 = 6
- Units: mm → 6 mm

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Problem 8: Find the height of parallelogram
- Given: Area = 56 in², base = 8 in
- Formula: Area = base × height → height = Area ÷ base
- Calculation: 56 ÷ 8 = 7
- Units: inches → 7 in

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Problem 9: Find the base of triangle
- Given: Area = 60 in², height = 8 in (since right angle at base-height corner)
- Formula: Area = (base × height) ÷ 2 → so base = (Area × 2) ÷ height
- Calculation: (60 × 2) ÷ 8 = 120 ÷ 8 = 15
- Units: inches → 15 in

*(Note: 17 in is the hypotenuse — not needed.)*

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Problem 10: Find the base of parallelogram
- Given: Area = 81 m², height = 18 m
- Formula: Area = base × height → base = Area ÷ height
- Calculation: 81 ÷ 18 = 4.5
- Units: meters → 4.5 m

*(Note: 11 m is a slant side — not needed.)*

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Problem 11: Find the height of triangle
- Given: Area = 34.5 ft², base = 12 ft
- Formula: Area = (base × height) ÷ 2 → height = (Area × 2) ÷ base
- Calculation: (34.5 × 2) ÷ 12 = 69 ÷ 12 = 5.75
- Units: feet → 5.75 ft

*(Sides 9 ft and 8 ft are not needed — they’re not the height.)*

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Problem 12: Find the base of triangle
- Given: Area = 72 in², height = 15 in (dashed line with right angle)
- Formula: Area = (base × height) ÷ 2 → base = (Area × 2) ÷ height
- Calculation: (72 × 2) ÷ 15 = 144 ÷ 15 = 9.6
- Units: inches → 9.6 in

*(Note: 17 in is another side — not needed.)*

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Final Answer:

1. 72 m²
2. 56 ft²
3. 12 in²
4. 42 in²
5. 14 ft²
6. 420
7. 6 mm
8. 7 in
9. 15 in
10. 4.5 m
11. 5.75 ft
12. 9.6 in