Educational geometry worksheet with shape identification and area calculation exercises.

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3. Motivation – Guessed the Shapes

Directions: Tell us the class the name of the different figures that can be seen in the house.

Looking at the image of the house:

- Roof: Triangle (specifically an isosceles triangle)
- Main body of the house: Rectangle
- Door: Rectangle (or possibly a rectangle with a semicircle on top, but here it's just a rectangle)
- Window: Square (yellow square)
- Arch above the door: Semicircle

So, the shapes present are:
- Triangle
- Rectangle
- Square
- Semicircle

✔ Answer:
- Triangle (roof)
- Rectangle (house body and door)
- Square (window)
- Semicircle (arch)

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4. APE – Analyze the figure and answer the question that follows:

We have a composite figure made up of:
- A trapezoid (quadrilateral) on top
- A triangle below it

The total height is 10 cm, and the trapezoid has a height of 6 cm. So the triangle must have a height of:

> 10 cm − 6 cm = 4 cm

Also, the base of the entire figure is 8 cm (as shown), and this applies to both the trapezoid and the triangle.

Let’s find the areas.

#### a) Area of the quadrilateral (trapezoid)

We need the formula for the area of a trapezoid:

> Area = $ \frac{1}{2} \times (b_1 + b_2) \times h $

But we don’t have two bases. Wait — looking closely at the figure, it appears the trapezoid is actually a rectangle on top of a triangle? Or is it a trapezoid?

Wait — actually, from the diagram:
- The top part is a trapezoid with parallel sides of 8 cm (top) and 10 cm (bottom), and height = 6 cm.
- But wait — the width of the whole shape is 8 cm, and the bottom base is wider than the top?

No — let’s re-express.

Actually, upon closer inspection, the figure seems to be a composite shape consisting of:
- A rectangle of height 6 cm and width 8 cm (top part)
- A triangle below it with base 8 cm and height 4 cm (since total height is 10 cm, and 10 − 6 = 4)

But the problem says "quadrilateral" and "triangle". So maybe the top is a trapezoid, not a rectangle?

Wait — if the top is a trapezoid with height 6 cm, and the base is 8 cm, and the top side is shorter, but we don't know the top length.

But in the diagram, it's shaded as a trapezoid with slanted sides. However, no dimensions are given for the top base.

Wait — actually, perhaps the quadrilateral is a trapezoid with:
- Height = 6 cm
- Two parallel sides: one is 8 cm (bottom), and the top side is unknown?

But we can't calculate without more info.

Alternatively, maybe the quadrilateral is a rectangle?

Let me reconsider.

Wait — perhaps the quadrilateral is the entire top portion, which looks like a trapezoid, but since it’s symmetric and has a flat top, maybe it’s a rectangle?

But the drawing shows a slanted roof, so the top part is a trapezoid.

But we need dimensions.

Wait — actually, the figure has:
- A trapezoid on top with:
- Height = 6 cm
- Bottom base = 8 cm
- Top base = ? Not labeled

Hmm — unless the top is 8 cm as well, then it would be a rectangle.

But the roof is sloped, so likely the top base is smaller.

But we don’t have enough data.

Wait — perhaps I misread.

Let’s look again.

The figure has:
- A large triangle or trapezoid?
- Actually, the top is a triangle?

No — the top is a quadrilateral with two slanted sides and two horizontal sides → that’s a trapezoid.

But we need the length of the top base.

Unless... the top base is 8 cm, same as bottom, then it's a rectangle.

But that doesn't make sense for a roof.

Wait — perhaps the quadrilateral is the upper part, which is a trapezoid with:
- Height = 6 cm
- Bottom base = 8 cm
- Top base = 8 cm? Then it's a rectangle.

But then the roof would be flat.

Wait — maybe the roof is a triangle?

But the problem says “quadrilateral” and “triangle”.

Ah! Now I see — the figure is composed of:
- A trapezoid (quadrilateral) on top
- A triangle below it

But the total height is 10 cm, and the trapezoid has height 6 cm, so the triangle has height 4 cm.

But what are the bases?

Let’s assume:
- The trapezoid has:
- Height = 6 cm
- Bottom base = 8 cm
- Top base = 8 cm → then it’s a rectangle → area = 8 × 6 = 48 cm²

Then the triangle has:
- Base = 8 cm
- Height = 4 cm
- Area = $ \frac{1}{2} \times 8 \times 4 = 16 $ cm²

Total area = 48 + 16 = 64 cm²

But is the top base really 8 cm?

If the roof is a triangle, then the top is a point.

But the problem says “quadrilateral”, so it must have four sides.

So the top part is a trapezoid, not a triangle.

Wait — maybe the quadrilateral is the whole upper section, which is a trapezoid with:
- Height = 6 cm
- Bottom base = 8 cm
- Top base = ? Let's say it's 4 cm (if symmetrical)

But we don’t have that value.

Alternatively, perhaps the quadrilateral is the rectangle and the triangle is the roof?

But the roof is a triangle.

Wait — maybe the quadrilateral is the rectangular base, and the triangle is the roof?

But the roof is above, and the figure shows a trapezoid?

I think there’s confusion.

Let’s re-read:

> What do you think is the total area of the quadrilateral?
> What do you think is the total area of the triangle?
> What is the total area of the two figures if combined?

And the figure shows:
- A trapezoid (quadrilateral) on top
- A triangle below it?

But the triangle is below the trapezoid?

That doesn’t make sense — usually the roof is on top.

Wait — maybe the quadrilateral is the lower part, and the triangle is the roof?

But the lower part is a rectangle, and the roof is a triangle.

But the roof is drawn as a triangle, and the lower part is a rectangle.

But the problem says “quadrilateral” and “triangle”.

So:
- Quadrilateral = rectangle (base of house)
- Triangle = roof

But the height of the quadrilateral is 6 cm, and the triangle has height 4 cm (since total height is 10 cm).

And the width is 8 cm.

So:
- Area of quadrilateral (rectangle) = length × width = 8 cm × 6 cm = 48 cm²
- Area of triangle = $ \frac{1}{2} \times base \times height = \frac{1}{2} \times 8 \times 4 = 16 $ cm²
- Total area = 48 + 16 = 64 cm²

✔ So answers:
- Area of quadrilateral: 48 cm²
- Area of triangle: 16 cm²
- Combined area: 64 cm²

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II. Presentation (A.A.)

#### A. Activity: Brainstorming

Now we’re given formulas and examples.

##### Area of a Square
> A = s × s
> Where s = side

Example: If side = 12 m, then area = 12 × 12 = 144 m²

##### Area of a Rectangle
> A = l × w
> Where l = length, w = width

Example: Length = 2 cm, Width = 1 cm → A = 2 × 1 = 2 cm²

##### Area of a Triangle
> A = $ \frac{1}{2} \times b \times h $
> Where b = base, h = height

Example: Base = 3 m, Height = 2 m → A = $ \frac{1}{2} \times 3 \times 2 = 3 $ m²

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✔ Final Answers:

#### 3. Shapes in the House:
- Triangle (roof)
- Rectangle (main body and door)
- Square (window)
- Semicircle (arch)

#### 4. APE – Area Calculations:
- Area of quadrilateral (rectangle): 48 cm²
- Area of triangle (roof): 16 cm²
- Combined area: 64 cm²

#### II. Presentation:
- Square: A = s² → 12×12 = 144 m²
- Rectangle: A = l×w → 2×1 = 2 cm²
- Triangle: A = ½×b×h → ½×3×2 = 3 m²

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