HSPT Math - Geometry | Practice Hub

Rectangle

Give the area of the above rectangle in square feet.

$216 \textrm{ ft}^{2}$

$532\textrm{ ft}^{2}$

$576 \textrm{ ft}^{2}$

$33 \textrm{ ft}^{2}$

$66 \textrm{ ft}^{2}$

Explanation

Since 1 yard = 3 feet, multiply each dimension by 3 to convert from yards to feet:

$8 \textrm{ yd} \times 3 \textrm{ ft/yd} = 24 \textrm{ ft}$

$3 \textrm{ yd} \times 3 \textrm{ ft/yd} = 9 \textrm{ ft}$

Use the area formula, substituting :

$A = 24 \times 9 = 216$ square feet

What is the area of the figure below?

Explanation

To find the area of the figure above, we need to slip the figure into two rectangles.

3.5

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=11\times 3$ $A=3\times 3$

To find our final answer, we need to add the areas together.

What is the area of the figure below?

6.5

Explanation

To find the area of the figure above, we need to slip the figure into two rectangles.

6.5

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=5\times 10$ $A=5\times 3$

To find our final answer, we need to add the areas together.

What is the area of the figure below?

Explanation

To find the area of the figure above, we need to slip the figure into two rectangles.

11.5

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=8\times 4$ $A=7\times 4$

To find our final answer, we need to add the areas together.

What is the area of the figure below?

Explanation

To find the area of the figure above, we need to slip the figure into two rectangles.

12.5

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=6\times 8$ $A=7\times 5$

To find our final answer, we need to add the areas together.

What is the area of the figure below?

Explanation

To find the area of the figure above, we need to slip the figure into two rectangles.

11.5

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=7\times 3$ $A=6\times 3$

To find our final answer, we need to add the areas together.

Find the area of a square if the length is .

Explanation

The area of a square is:

Substitute the length and simplify.

Spinner target

Above is a target. The radius of the smaller quarter-circles is half that of the larger quarter-circles.

A blindfolded man throws a dart at the above target. Assuming the dart hits the target, and that no skill is involved, give the odds against the dart landing in the yellow region.

39 to 1

13 to 1

14 to 1

40 to 1

Explanation

Call the radius of one of the smaller quarter-circles 1 (the reasoning is independent of the actual radius). Then the area of each quarter-circle is

$\frac{1}{4} \cdot \pi r ^{2} = \frac{1}{4} \cdot \pi \cdot 1 ^{2} = \frac{1}{4} \pi$ .

Each of the four wedges of one such quarter-circle has area

$\frac{1}{4} \cdot \frac{1}{4} \pi = \frac{\pi}{16}$ .

The yellow region is one such wedge.

The radius of each of the larger quarter-circles is 2, so the area of each is $\frac{1}{4} \cdot \pi r ^{2} = \frac{1}{4} \cdot \pi \cdot 2 ^{2} = \pi$