Lesson: Geometry Intermediate - 12t01

Area Of A Quadrilateral, Continued

Task: Select the correct answer and then click Continue.

If all angles in the figure above are right angles, what is the area of the figure?

	34
	40
	42
	48
	52

The figure in this question is not a quadrilateral, but it is composed of a number of quadrilaterals. A glance at the diagram will show that the figure can be broken into three rectangles — a small one at the top, a small one of equal size at the bottom, and another vertically-oriented rectangle in the middle. If we knew the dimensions of each, we could find the total area easily. But we're only given some of the dimensions, so we'll need to use what we're given to find the rest. Let's begin with the vertical lengths:

Vertical lengths: The only vertical length we're missing is the length of the longest vertical segment on the right side (the 'cut out' side) of the figure. Since the figure has a total height of 12 and we're given the 2 other vertical lengths as being 2 and 2, this length must equal 12 – (2 + 2) = 12 – 4 = 8.

Horizontal lengths: We're missing two horizontal lengths from the small rectangle at the bottom of the figure. But, according to the diagram, the dimensions of this rectangle correspond to the dimensions of the uppermost rectangle. Therefore, missing lengths are 1 and 4 (see diagram above).

We can now compute the area: The top rectangle has a length of 4 and a height of 2 for an area of 4 × 2 = 8 The middle rectangle has a length of 4 – 1 = 3 and a width of 8 for an area of 3 × 8 = 24. The bottom rectangle has a length of 4 and a height of 2 for an area of 4 × 2 = 8.

The total area of the figure is 8 + 24 + 8 = 40. Choice (B) is correct.

Next to display next topic in the chapter.