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100 POINTS HELP ASAP!!!

Given
Base1 = 10ft
Base2 =__ft
Height of the Trapezoid =__ft
Area of the Trapezoid = __ft2
Volume of the Trapezoidal Prism =___ft3

100 POINTS HELP ASAP Given Base1 10ft Base2 ft Height of the Trapezoid ft Area of the Trapezoid ft2 Volume of the Trapezoidal Prism ft3 class=

Respuesta :

msm555

Answer:

Base 1 = 10 ft

Base 2 = 13 ft

Height of the Trapezoid = 7 ft

Area of the Trapezoid = 80.5 ft²

Volume of the Trapezoidal Prism = 1207.5 ft³

Step-by-step explanation:

Let's calculate the missing values step by step.

Area of the Trapezoid:

The formula for the area (A) of a trapezoid is:

[tex] \boxed{\boxed{ \sf \textsf{Area of trapezoid} = \dfrac{1}{2} \times (Base_1 + Base_2) \times Height}}[/tex]

Given:

  • Base 1 (b1) = 10 ft
  • Base 2 (b2) = 13 ft
  • Height (h) = 7 ft

Substitute these values into the area formula:

[tex] \sf Area = \dfrac{1}{2} \times (10 \textsf{ ft} + 13 \textsf{ ft}) \times 7 \textsf{ ft} [/tex]

[tex] \sf Area = \dfrac{1}{2} \times 23 \textsf{ ft} \times 7 \textsf{ ft} [/tex]

[tex] \sf Area = \dfrac{1}{2} \times 161 \textsf{ ft}^2 [/tex]

[tex] \sf Area = 80.5 \textsf{ ft}^2 [/tex]

Therefore, the area of the trapezoid is:

[tex]\large \bold{\sf\boxed{ \boxed{80.5 \textsf{ ft}^2} }}[/tex]

Volume of the Trapezoidal Prism

To find the volume (V) of a trapezoidal prism, we multiply the area of the trapezoid (base area) by the height of the prism.

Given:

  • Height of the trapezoid prism (h_prism) = 15 ft

Using the area of the trapezoid we calculated:

[tex] \boxed{\boxed{\sf Volume = \textsf{Base Area} \times \textsf{Height of Prism} }}[/tex]

[tex] \sf Volume = 80.5 \textsf{ ft}^2 \times 15 \textsf{ ft} [/tex]

[tex] \sf Volume = 1207.5 \textsf{ ft}^3 [/tex]

Therefore, the volume of the trapezoidal prism is:

[tex]\Large\boxed{\sf \boxed{1207.5 \textsf{ ft}^3} }[/tex]

In summary:

Base 1 = 10 ft

Base 2 = 13 ft

Height of the Trapezoid = 7 ft ( which is perpendicular to two parallel lines of trapezoid)

Area of the Trapezoid = 80.5 ft²

Volume of the Trapezoidal Prism = 1207.5 ft³

Ver imagen msm555
semsee45

Answer:

Base 1 = 10 ft

Base 2 = 13 ft

Height of the Trapezoid = 7 ft

Area of the Trapezoid = 80.5 ft²

Volume of the Trapezoidal Prism = 1,207.5 ft³

Step-by-step explanation:

The given diagram shows a trapezoidal prism, consisting of two congruent trapezoid bases and rectangular or parallelogram faces connecting them.

[tex]\dotfill[/tex]

Bases of the Trapezoid

A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs.

In this case, the parallel sides (bases) of the trapezoid base of the prism measure 10 ft and 13 ft, so:

[tex]\Large\boxed{\textsf{Base 1} = 10 \sf \; ft}[/tex]

[tex]\Large\boxed{\textsf{Base 2} = 13 \sf \; ft}[/tex]

[tex]\dotfill[/tex]

Height of the Trapezoid

The height of a trapezoid is the perpendicular distance between the two parallel bases of the trapezoid. As the leg of the trapezoid that measures 7 ft is perpendicular to both the bases, this is the height of the trapezoid. Therefore:

[tex]\Large\boxed{\textsf{Height of the Trapezoid} = 7 \sf \; ft}[/tex]

[tex]\dotfill[/tex]

Area of the Trapezoid

The formula to the area of a trapezoid is:

[tex]\boxed{\begin{array}{l}\underline{\textsf{Area of a trapezoid}}\\\\A=\dfrac{1}{2}h(b_1+b_2)\\\\\textsf{where:}\\ \phantom{ww}\bullet\;\textsf{$A$ is the area.}\\ \phantom{ww}\bullet\;\textsf{$b_1$ and $b_2$ are the parallel sides (bases).}\\\phantom{ww}\bullet\;\textsf{$h$ is the height (perpendicular to the bases).}\end{array}}[/tex]

Therefore, to find the area of the trapezoid, substitute b₁ = 10, b₂ = 13 and h = 7 into the area formula:

[tex]A=\dfrac{1}{2} \cdot 7(10+13)\\\\\\A=\dfrac{1}{2} \cdot 7(23)\\\\\\A=\dfrac{1}{2} \cdot 161\\\\\\A=80.5\; \sf ft^2[/tex]

So, the area of the trapezoid is:

[tex]\Large\boxed{\textsf{Area of the Trapezoid} =80.5 \sf \; ft^2}[/tex]

[tex]\dotfill[/tex]

Volume of the Trapezoidal Prism

To find the volume of a prism, we multiply the area of one of its bases by its height.

In this case, the area of the base of the prism is the area of the trapezoid (80.5 ft²) and the height of the prism is 15 ft. Therefore:

[tex]V=\textsf{Area of base}\times \textsf{Height}\\\\V=80.5 \times15\\\\V=1207.5\; \sf ft^3[/tex]

So, the volume of the trapezoidal prism is:

[tex]\Large\boxed{\textsf{Volume of the Trapezoidal Prism} =1207.5 \sf \; ft^3}[/tex]

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