Respuesta :

joseaaronlara

Answer:

The answer to your question is Area = 24, letter B

Step-by-step explanation:

Data

ABCD is a rectangle

BE = 4

DC = 12

CE = 5

Process

1.- Calculate the area of the ΔABD

Area ΔABD = base x height /2

                   = 12 x (5 + 4) /2

                   = 12 x 9/2

                   = 54

2.- Calculate the area of the ΔCDE

Area ΔCDE = 12 x 5/2

                   = 30

3.- Calculate the area of the rectangle ABCD

Area = 12 x 9

        = 108

4.- Find the area of the ΔBDE

Area = A rectangle - A ΔABD - A ΔCDE

Area = 108 - 54 - 30

Area = 24

Answer: option B is the correct answer.

Step-by-step explanation:

In a rectangle, the opposite sides are equal. The diagonal, BD divides the rectangle into 2 equal right angle triangles.

To determine the area of BCD, we would apply the formula for determining the area of a triangle which is expressed as

Area = 1/2 × base × height

Base = 12

Height = 5 + 4 = 9

Area = 1/2 × 12 × 9 = 54

Area of triangle CDE would be

Area = 1/2 × 12 × 5 = 30

Therefore, area of triangle BED = area of triangle BCD - area of triangle CDE

Area of triangle BED = 54 - 30 = 24

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