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soldi70 [24.7K]
3 years ago
11

Pls help its due today

Mathematics
1 answer:
Salsk061 [2.6K]3 years ago
7 0

Answer:

\boxed{Area \: of \: trapezium = 72 \: {cm}^{2}}

Step-by-step explanation:

Area \: of \: trapezoid =  \frac{1}{2} (sum \: of \: parallel \: sides) \times height

Parallel sides are = 9 cm and 15 cm

Height = 6 cm

Area \: of \: trapezium =  \frac{1}{2}(9 + 15) \times 6 \\  \\  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:    \:  \:  =  \frac{1}{2 }   \times 24 \times 6 \\  \\   \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   = 12  \times 6 \\  \\  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   \:  \:  = 72  \: {cm}^{2}

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So, all the possible areas are given by the product of the dimensions, i.e.

x(10-x) = -x^2+10x

The function f(x)=-x^2+10x represents a parabola, facing downwards, and thus it admits a maximum, which is its vertex.

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