Quadrilaterals

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Geometry › Quadrilaterals

Questions 1 - 10

Know that in a Major League Baseball infield the distance between home plate and first base is 90 feet and the infield is a perfect square.

What is the area of a Major League Baseball infield?

$8100\ ft^2$

$90\ ft^2$

$900\ ft^2$

$360\ ft^2$

$180\ ft^2$

Explanation

Because the infield is a square, the distance between each set of bases is 90 feet.

To find the area of a square you multiply the length by the width.

In this case

$90\times90=8100\ ft^2$ .

Find the length of a side of a rhombus that has diagonal lengths of and .

Explanation

Recall that in a rhombus, the diagonals are not only perpendicular to each other, but also bisect one another.

Thus, we can find the lengths of half of each diagonal and use that in the Pythagorean Theorem to find the length of the side of the rhombus.

First, find the lengths of half of each diagonal.

$\text{Half Diagonal 1}=\frac{12}{2}=6$

$\text{Half Diagonal 2}=\frac{14}{2}=7$

Now, use these half diagonals as the legs of a right triangle that has the side of the rhombus as its hypotenuse.

$\text{Side of Rhombus}=\sqrt{(\text{Half Diagonal 1})^2+(\text{Half Diagonal 2})^2}$

Plug in the lengths of the half diagonals to find the length of the rhombus.

$\text{Side of Rhombus}=\sqrt{6^2+7^2}=\sqrt{85}=9.22$

Make sure to round to places after the decimal.

Which of the following shapes is a trapezoid?

Shapes

Explanation

A trapezoid is a four-sided shape with straight sides that has a pair of opposite parallel sides. The other sides may or may not be parallel. A square and a rectangle are both considered trapezoids.

An isosceles trapezoid has two bases that are parallel to each other. The larger base is times greater than the smaller base. The smaller base has a length of inches and the length of non-parallel sides of the trapezoid have a length of inches.

What is the perimeter of the trapezoid?

Explanation

To find the perimeter of this trapezoid, first find the length of the larger base. Then, find the sum of all of the sides. It's important to note that since this is an isosceles trapezoid, both of the non-parallel sides will have the same length.

The solution is:

The smaller base is equal to inches. Thus, the larger base is equal to:

$2.5\times4=10$

, where the length of one of the non-parallel sides of the isosceles trapezoid.

$P=2.5+10+(2\times 4.5)$

Find the area of a square if its diagonal is $5\sqrt3$

$\frac{75}{2}$

$\frac{75\sqrt3}{2}$

$75\sqrt2$

$75\sqrt6$

Explanation

The diagonal of a square is also the hypotenuse of a triangle.

Recall how to find the area of a square:

$\text{Area}=\text{side}^2$

Now, use the Pythagorean theorem to find the area of the square.

$\text{side}^2+\text{side}^2=\text{Diagonal}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{Area}=\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Plug in the length of the diagonal to find the area of the square.

$\text{Area}=\frac{(5\sqrt3)^2}{2}=\frac{75}{2}$

A parallelogram has a height of and an area of . What is the length of the base of the parallelogram?

Explanation

To find the missing side of this parallelgram apply the formula: $A=base\times height$

Thus, the solution is:

$168=12\times base$

$base=\frac{168}{12}=14$

A square has diagonals of length 1. True or false: the area of the square is $\frac{1}{2}$ .

True

False

Explanation

Since a square is a rhombus, its area is equal to half the product of the lengths of its diagonals. Each diagonal has length 1, so the area is equal to

$A = \frac{1}{2} \cdot 1 \cdot 1 = \frac{1}{2}$ .