Student's completed area calculation worksheet with step-by-step solutions and highlighted work.

Let’s solve each problem step by step.

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Problem 1: Area of triangle TRI

We are given:
- Base = 18 (side TI)
- Height = 20 (the perpendicular distance from R to line TI — shown with the yellow dashed line and right angle symbol)

Formula for area of a triangle:
> Area = ½ × base × height

Plug in the numbers:
Area = ½ × 18 × 20
First, ½ × 18 = 9
Then, 9 × 20 = 180

✔ So, area is 180 square units.

*(Note: The side labeled “22” is not needed here — it’s a slant side, not the height. We only use the perpendicular height.)*

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Problem 2: Area of rectangle RECT

We are told it’s a rectangle, so opposite sides are equal and all angles are 90°.

Given:
- Side RT = 11 (height)
- Diagonal RC = 15
- We need to find the length of side TC (base), then multiply by height to get area.

Use Pythagorean Theorem on triangle RTC (right triangle at T):

> (TC)² + (RT)² = (RC)²
> (TC)² + 11² = 15²
> (TC)² + 121 = 225
> (TC)² = 225 - 121 = 104
> TC = √104

Simplify √104:
√104 = √(4 × 26) = 2√26

Now, area of rectangle = base × height = TC × RT = 2√26 × 11 = 22√26

✔ So, area is 22√26 square units.

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Problem 3: Length of side GR in parallelogram GRAM

We’re told:
- Area of parallelogram GRAM = 72 sq. cm
- One side GM = 10
- A segment from G down to side MA has length 8 (this is the height corresponding to base MA)
- Also, part of base MA is labeled as 6 (from M to foot of perpendicular)

Wait — let’s clarify:

In a parallelogram, area = base × height.

The diagram shows:
- From point G, a perpendicular drops to side MA, meeting it at some point (let’s call it P). GP = 8 (height).
- MP = 6 (part of the base).
- But we don’t know the full base MA yet.

Actually, looking again — the problem asks for length of side GR.

In parallelogram GRAM:
- Opposite sides are equal → GR = MA, and GM = RA = 10.
- So if we can find length of MA, that equals GR.

But wait — maybe they want us to use the area formula directly?

Area = base × height

If we take base = MA, and height = 8 (perpendicular from G to MA), then:

72 = MA × 8
→ MA = 72 ÷ 8 = 9

Since GR = MA (opposite sides of parallelogram), then GR = 9

✔ So, length of side GR is 9 cm.

*(Note: The “use Pyth.” note might be confusing — but actually, we don’t need it here because the height is already given as 8, and area is given. The 6 and 10 may be red herrings or for another part — but since area and height are known, we can directly find base.)*

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Final Answer:
1. 180
2. 22√26
3. 9