Question

22 Calendario matemático ABCD cuadrado de lado 12cm
determine el área del cuadrilátero sombreado
gracias! ​

Answer 1

Respuesta:

El area sombreada es de 45cm²

Explicación paso a paso:

Lado del  cuadrado = 12cm

Area cuadrado = Lado * Lado = (12cm)(12cm) = 144cm²

Area del cuadrado de lado 4cm = 4cm * 4cm = 16cm²

Area cuadrado de lado 2cm = 2cm * 2cm = 4cm²

Area cuadrado de lado = 1cm = 1cm * 1cm = 1cm²

Area cuadrado de lado 3cm = (3cm)(3cm) = 9cm²

Area trapecio = At = (base mayor + base menor) * Altura/2

At 1 = (4cm + 2cm) *6cm/2 = (6cm)(6cm)/2 = 36cm²/2 = 18cm²

At 2 = (3cm + 2cm) * 7cm/2 = (5cm)(7cm)/2 = 35cm²/2 = 17,5cm²

At 3 = (3cm + 1cm) * 8cm/2 = (4cm)(8cm)/2 = 32cm²/2 = 16cm²

At4 = (4cm + 1cm) * 7cm/2 = (5cm)(7cm)/2 = 35cm²/2 = 17,5cm²

Area sombreada = As

As =Area del cuadrado ABCD - Area de 4cuadrado - Area de 4 trapecios

As = 144 - 16 - 4 - 9 - 1 - 18 - 17,5 - 16 - 17.5

AS = 144 - 99 = 45cm²

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