How to Find x in Fractions + Area of a Composite (T‑Shaped) Figure

Problems that ask you to find a missing length x (in fractions) and then find the area of a composite (irregular) shape show up a lot in Grades 5–12. The trick is to treat the diagram like a puzzle: use the total width/height to solve for missing parts, then split the shape into easy rectangles.

The example problem (worksheet photo)

In this example, the worksheet asks two things:

• Find x in fractions (a missing horizontal length)
• Find the area in decimals (of the full T-shaped figure)

Step 1: Find the missing length x (fractions)

The top width is 11 5/8. That total width is made of three horizontal pieces:

• 4 3/4 (left overhang)
• 3 1/3 (stem width)
• x (right overhang)

So the equation is:

Convert to improper fractions (optional but clean)

• 11 5/8 = 93/8
• 4 3/4 = 19/4
• 3 1/3 = 10/3

Use a common denominator

A common denominator for 8, 4, and 3 is 24:

• 93/8 = 279/24
• 19/4 = 114/24
• 10/3 = 80/24

Now subtract to solve for x:

Step 2: Find the area (in decimals)

Split the T-shape into two rectangles:

• Top bar: width 11 5/8 and height 3.2
• Stem: width 3 1/3 and height (7.1 − 3.2) = 3.9

Rectangle A (top bar)

• 11 5/8 = 11.625
• Area = 11.625 × 3.2 = 37.2

Rectangle B (stem)

• 3 1/3 = 10/3 ≈ 3.333…
• Area = (10/3) × 3.9 = 13

Total area

Add the two rectangle areas:

Common mistakes (and how to avoid them)

• Forgetting what the total width represents: make sure you’re adding/subtracting horizontal segments that line up on the same straight line.
• Mixing mixed numbers and improper fractions: pick one format (often improper fractions) and stick with it.
• Using the wrong stem height: the stem height is the total height minus the top bar height (here: 7.1 − 3.2).
• Accidentally double-counting area: splitting into rectangles should cover the shape exactly once (no overlaps).

See what Gradulo's feedback looks like

Here's the kind of step-by-step feedback you can get after uploading a photo.

Fastest way to “check my work”

If you want a teacher-style check (not just an answer), upload a clear picture of your worksheet and include your steps. Gradulo will point out what's correct, what needs fixing, and what to do next.

• Check my work from a photo (conversion page + example)
• Try the photo demo