Geometry worksheet for calculating area and perimeter of basic shapes.

Let’s solve each problem one by one, step by step.

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Problem 1: Find the area of a rectangle with length 16 cm and width 10 cm.

Area of a rectangle = length × width
So, 16 cm × 10 cm = 160 cm²

✔ Check: 16 × 10 is indeed 160. Units are square centimeters because it’s area.

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Problem 2: Find the area of a square with side 12 cm.

Area of a square = side × side
So, 12 cm × 12 cm = 144 cm²

✔ Check: 12 × 12 = 144. Correct.

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Problem 3: Find the area of a triangle with base 18 cm and height 10 cm.

Area of a triangle = (base × height) ÷ 2
So, (18 cm × 10 cm) ÷ 2 = 180 ÷ 2 = 90 cm²

✔ Check: 18 × 10 = 180; half of that is 90. Correct.

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Problem 4: Find the perimeter of rectangle ABCD where AB = 5 m and AC = 9 m.

Wait — let’s look carefully.

In rectangle ABCD:

- Points A, B, C, D are corners.
- AB is one side → given as 5 m.
- AC is labeled as 9 m — but in a rectangle, AC would be a diagonal if A and C are opposite corners.

But wait — in standard labeling of rectangles:

If it’s labeled A—B
| |
D—C

Then AB and DC are top and bottom sides, AD and BC are left and right sides.

But here, they say AB = 5m and AC = 9m.

If A to C is a diagonal, then we can’t directly use it for perimeter unless we find the other side.

BUT — looking at the diagram description: It says “AB = 5m” and “AC = 9m”, and shows points A, B, C, D arranged as a rectangle with A top-left, B bottom-left, C top-right, D bottom-right? Wait — that doesn’t make sense because then AC would be horizontal top side.

Actually, re-examining typical labeling:

Usually, rectangle is labeled clockwise: A (top-left), B (bottom-left), C (bottom-right), D (top-right)? No — that’s not standard.

Standard is: A (top-left), B (top-right), C (bottom-right), D (bottom-left). Then AB is top side, BC is right side, etc.

But in the problem, it says:

“AB = 5m” and “AC = 9m”

And the figure has points A, B, C, D with lines connecting them as a rectangle.

If AB is one side (say, vertical or horizontal), and AC is another side — but in a rectangle, adjacent sides meet at corners.

Wait — perhaps there's a typo or mislabeling? Let me think differently.

Looking again: The problem says “Find the perimeter.” and gives AB = 5m and AC = 9m.

But in a rectangle, if A and B are adjacent, and A and C are also adjacent, then angle at A is 90 degrees, so AB and AC would be two adjacent sides.

That makes sense! So maybe point C is adjacent to A, meaning the rectangle has sides AB and AC meeting at A.

So if AB = 5m and AC = 9m, and they are perpendicular (since it’s a rectangle), then those are the two different side lengths.

Therefore, the rectangle has sides 5m and 9m.

Perimeter of rectangle = 2 × (length + width) = 2 × (5 + 9) = 2 × 14 = 28 meters

✔ Check: Yes, if two adjacent sides are 5 and 9, then perimeter is 2*(5+9)=28. Makes sense.

(Note: If AC were a diagonal, we’d need Pythagoras, but since no indication of that and the numbers work out nicely as sides, this must be intended.)

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Final Answer:
1. 160 cm²
2. 144 cm²
3. 90 cm²
4. 28 m