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1 Calculate the perimeter of the shape below? 2 the shape below is called a?

Mathematics

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Calculate the perimeter of the shape below?

The shape is a composite figure consisting of a rectangle and a right-angled triangle.
The top side of the rectangle is 16 cm16 \text{ cm}.
The slanted side of the triangle is 8 cm8 \text{ cm}.
The tick marks on the right vertical side of the rectangle and the base of the triangle indicate that these two lengths are equal. Let's call this common length xx. So, the height of the rectangle is xx, and the base of the triangle is xx.

  1. Identify the lengths of the sides for the perimeter.

    • Top horizontal side: 16 cm16 \text{ cm}
    • Right vertical side: x cmx \text{ cm}
    • Bottom horizontal side: 16 cm16 \text{ cm} (from the rectangle part) +x cm+ x \text{ cm} (from the triangle part) =(16+x) cm= (16 + x) \text{ cm}
    • Left slanted side: 8 cm8 \text{ cm}

  2. Use the Pythagorean theorem to find xx.

    The triangle is a right-angled triangle with legs xx and xx, and hypotenuse 8 cm8 \text{ cm}.

    x2+x2=82x^2 + x^2 = 8^2 2x2=642x^2 = 64 x2=642x^2 = \frac{64}{2} x2=32x^2 = 32 x=32x = \sqrt{32} x=16×2x = \sqrt{16 \times 2} x=42 cmx = 4\sqrt{2} \text{ cm}

  3. Calculate the perimeter by adding all the side lengths.

    Perimeter=16 cm+x cm+(16+x) cm+8 cm\text{Perimeter} = 16 \text{ cm} + x \text{ cm} + (16 + x) \text{ cm} + 8 \text{ cm}

    Substitute x=42 cmx = 4\sqrt{2} \text{ cm}:

    Perimeter=16+42+(16+42)+8\text{Perimeter} = 16 + 4\sqrt{2} + (16 + 4\sqrt{2}) + 8 Perimeter=16+42+16+42+8\text{Perimeter} = 16 + 4\sqrt{2} + 16 + 4\sqrt{2} + 8 Perimeter=(16+16+8)+(42+42)\text{Perimeter} = (16 + 16 + 8) + (4\sqrt{2} + 4\sqrt{2}) Perimeter=40+82 cm\text{Perimeter} = 40 + 8\sqrt{2} \text{ cm}

    The perimeter of the shape is \boxed{\text{40 + 8\sqrt{2} cm}}.

Part 2

The shape below is called a?

The shape shown is a three-dimensional object with two circular bases and a curved surface connecting them.
The shape is called a cylinder.
The shape is a cylinder\boxed{\text{cylinder}}.

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