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Calculate the surface area of a square based pyramid with base side length 9 cm and slant height 14 cm.

Mathematics

ScanSolve AI Answer

Answer

333 cm2333 \text{ cm}^2

Step-by-step solution

4 steps
  1. Tambua vipimo vya piramidi.

    Piramidi ina msingi wa mraba wenye urefu wa upande (ss) wa 9 cm9 \text{ cm}.
    Urefu mteremko (ll) wa nyuso za pembeni ni 14 cm14 \text{ cm}.

  2. Kokotoa eneo la msingi.

    Msingi ni mraba.

    Amsingi=s2=(9 cm)2=81 cm2A_{msingi} = s^2 = (9 \text{ cm})^2 = 81 \text{ cm}^2
  3. Kokotoa eneo la nyuso nne za pembeni (triangles).

    Kila uso wa pembeni ni pembetatu yenye msingi s=9 cms = 9 \text{ cm} na urefu mteremko l=14 cml = 14 \text{ cm}.
    Eneo la pembetatu moja = 12×msingi×urefu mteremko\frac{1}{2} \times \text{msingi} \times \text{urefu mteremko}

    Apembetatu=12×9 cm×14 cm=9 cm×7 cm=63 cm2A_{pembetatu} = \frac{1}{2} \times 9 \text{ cm} \times 14 \text{ cm} = 9 \text{ cm} \times 7 \text{ cm} = 63 \text{ cm}^2

    Eneo la nyuso nne za pembeni = 4×Apembetatu4 \times A_{pembetatu}

    Apembeni=4×63 cm2=252 cm2A_{pembeni} = 4 \times 63 \text{ cm}^2 = 252 \text{ cm}^2
  4. Kokotoa jumla ya eneo la uso la piramidi.

    Jumla ya eneo la uso (AjumlaA_{jumla}) ni jumla ya eneo la msingi na eneo la nyuso nne za pembeni.

    Ajumla=Amsingi+ApembeniA_{jumla} = A_{msingi} + A_{pembeni} Ajumla=81 cm2+252 cm2A_{jumla} = 81 \text{ cm}^2 + 252 \text{ cm}^2 Ajumla=333 cm2A_{jumla} = 333 \text{ cm}^2 333 cm2333 \text{ cm}^2
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