Question

Find the area of the quadrilateral in the figure.

Answer 1

Answer:

C. 19.64

Explanation:

The triangle at upper right is a 3-4-5 right triangle, so has an area that is half the product of the leg lengths:

... upper right area = (1/2)(3 units)(4 units) = 6 units²

The triangle at lower left is an isosceles triangle with base length 5 and side length 6. The altitude to the side of length 5 is a bisector of that side and forms right angles at the point of intersection. Hence we can use the Pythagorean theorem to find the triangle's altitude:

... lower left triangle altitude = √(6² - 2.5²) = √29.75 ≈ 5.45436

Then the area of the lower left triangle is half the product of this altitude and the base length of 5 units:

... lower left area = (1/2)(5.45436 units)(5 units) ≈ 13.6359 units²

The quadrilateral's area is the sum of the areas of these triangles, so is ...

... quadrilateral area = upper right area + lower left area

... = 6 units² + 13.6359 units²

... = 19.6359 units² ≈ 19.64 units²

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Confirmed by my geometry program as shown in the attachment.