Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm. ​

Step-by-step explanation:

The quadrilateral ABCD consists of two triangles. By adding the area of the two triangles, we get the area of the entire quadrilateral.

Vertices A, B, and C form a right triangle with legs , , and . The two legs, 3 and 4, represent the triangle's height and base, respectively.

The area of a triangle with base and height is given by . Therefore, the area of this right triangle is:

The other triangle is a bit trickier. Triangle is an isosceles triangles with sides 5, 5, and 4. To find its area, we can use Heron's Formula, given by:

, where , , and are three sides of the triangle and is the semi-perimeter ().

The semi-perimeter, , is:

Therefore, the area of the isosceles triangle is:

Thus, the area of the quadrilateral is:

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step-by-step explanation:

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step-by-step explanation:

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