Question

The next castle paul Wants to build starts with a square prism with a side length of 42 inches. This is topped by a smaller square prism with a side length of 30 inches. On the very top is a triangular pyramid. The area of the base of the triangular pyramid is 144 square inches, and the height of the pyramid is 18 inches.
How much sand does this castle require?

Answer 1

Answer:

Answer:

240 cm² is the required area of Trapezium.

Step-by-step explanation:

According to the Question

It is given that,

Length of Parallel side 15 & 25 cm

Distance between them ,h = 12cm

we have to calculate the area of trapezium .

As we know that ,

Area of Trapezium = ½ × (sum of parallel side) × distance between them

On substituting the value we get

↠ Area of Trapezium = ½ × (15+25) × 12

↠ Area of Trapezium = ½ × (40) × 12

↠ Area of Trapezium = 20 × 12

↠ Area of Trapezium = 240 cm²

Hence, the area of trapezium is 240cm².

Additional Information !!

\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}

FormulasofAreas:−

⋆Square=(side)

2

⋆Rectangle=Length×Breadth

⋆Triangle=

2

1

×Breadth×Height

⋆Scalene△=

s(s−a)(s−b)(s−c)

⋆Rhombus=

2

1

×d

1

×d

2

⋆Rhombus=

2

1

d

4a

2

−d

2

⋆Parallelogram=Breadth×Height

⋆Trapezium=

2

1

(a+b)×Height

⋆EquilateralTriangle=

4

3

(side)

2