HSPT Math › Geometry
What is the area of the figure below?
To find the area of the figure above, we need to slip the figure into two rectangles.
Using our area formula, , we can solve for the area of both of our rectangles
To find our final answer, we need to add the areas together.
The ratio of the perimeter of one square to that of another square is . What is the ratio of the area of the first square to that of the second square?
For the sake of simplicity, we will assume that the second square has sidelength 1; Then its perimeter is , and its area is
.
The perimeter of the first square is , and its sidelength is
. The area of this square is therefore
.
The ratio of the areas is therefore .
What is the slope of the line that passes through and
?
We can use the slope formula:
What is the area of the figure below?
To find the area of the figure above, we need to slip the figure into two rectangles.
Using our area formula, , we can solve for the area of both of our rectangles
To find our final answer, we need to add the areas together.
What angle is complement to ?
The complement to an angle is ninety degrees subtract the angle since two angles must add up to 90. In this case, since we are given the angle in radians, we are subtracting from instead to find the complement. The conversion between radians and degrees is:
Reconvert the fractions to the least common denominator.
Reduce the fraction.
What angle is complement to ?
The complement to an angle is ninety degrees subtract the angle since two angles must add up to 90. In this case, since we are given the angle in radians, we are subtracting from instead to find the complement. The conversion between radians and degrees is:
Reconvert the fractions to the least common denominator.
Reduce the fraction.
A certain cube has a side length of 25 m. How many square tiles, each with an area of 5 m2, are needed to fully cover the surface of the cube?
100
200
500
750
1000
A cube with a side length of 25m has a surface area of:
25m * 25m * 6 = 3,750 m2
(The surface area of a cube is equal to the area of one face of the cube multiplied by 6 sides. In other words, if the side of a cube is s, then the surface area of the cube is 6_s_2.)
Each square tile has an area of 5 m2.
Therefore, the total number of square tiles needed to fully cover the surface of the cube is:
3,750m2/5m2 = 750
Note: the volume of a cube with side length s is equal to _s_3. Therefore, if asked how many mini-cubes with side length n are needed to fill the original cube, the answer would be:
s3/n3
What is the area of the figure below?
To find the area of the figure above, we need to slip the figure into two rectangles.
Using our area formula, , we can solve for the area of both of our rectangles
To find our final answer, we need to add the areas together.
What is the area of the figure below?
To find the area of the figure above, we need to slip the figure into two rectangles.
Using our area formula, , we can solve for the area of both of our rectangles
To find our final answer, we need to add the areas together.
A certain cube has a side length of 25 m. How many square tiles, each with an area of 5 m2, are needed to fully cover the surface of the cube?
100
200
500
750
1000
A cube with a side length of 25m has a surface area of:
25m * 25m * 6 = 3,750 m2
(The surface area of a cube is equal to the area of one face of the cube multiplied by 6 sides. In other words, if the side of a cube is s, then the surface area of the cube is 6_s_2.)
Each square tile has an area of 5 m2.
Therefore, the total number of square tiles needed to fully cover the surface of the cube is:
3,750m2/5m2 = 750
Note: the volume of a cube with side length s is equal to _s_3. Therefore, if asked how many mini-cubes with side length n are needed to fill the original cube, the answer would be:
s3/n3