How to find a triangle on a coordinate plane

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ISEE Lower Level Quantitative Reasoning › How to find a triangle on a coordinate plane

Questions 1 - 10

1

Vt_custom_xy_xytriangle3

The triangle shown above has a base of and height of . Find the perimeter of the triangle.

$21+\sqrt{233}$

$\sqrt{233}$

$21+\sqrt{33}$

Explanation

The perimeter of this triangle can be found using the formula: $P=height + base +\sqrt{height^2 +base^2}$

Thus, the solution is:

$P=13+8+\sqrt{8^2+13^2}$
$P=21 +\sqrt{64+169}$
$P=21+\sqrt{233}$

2

Vt_custom_xy_xytriangle_1

Find the area of the above triangle--given that it has a base of and a height of .

square units

square units

square units

square units

Explanation

To find the area of the right triangle apply the formula: $A=\frac{base\times height}{2}$

Thus, the solution is:

$A=\frac{6\times 8}{2}=\frac{48}{2}=24$

3

Vt_custom_xy_xytriangle3

The triangle shown above has a base of and height of . Find the length of the longest side of the triangle (the hypotenuse).

$\sqrt{233}$

$\sqrt{64}$

$\sqrt{169}$

Explanation

In order to find the length of the longest side of the triangle (hypotenuse), apply the formula:

, where and are equal to and , respectively. And, the hypotenuse.

Thus, the solution is:

$c=\sqrt{233}$

4

Vt_custom_xy_xytriangle3

The triangle shown above has a base of and height of . Find the area of the triangle.

square units

square units

square units

square units

Explanation

To find the area of this triangle apply the formula: $A=\frac{base\times height}{2}$

Thus, the solution is:

$A=\frac{13\times 8}{2}=\frac{104}{2}=52$

5

Vt_custom_xy_xytriangle_4

The above triangle has a height of and a base with length . Find the area of the triangle.

square units

square units

square units

square units

Explanation

In order to find the area of this triangle apply the formula: $A=\frac{base \times height}{2}= \frac{4\times 3}{2}=\frac{12}{2}=6$

6

Vt_custom_xy_xytriangle2

The above triangle has a base of and a height of . Find the area.

square units

square units

square units

square units

Explanation

To find the area of this right triangle apply the formula: $A=\frac{base \times height}{2}$

Thus, the solution is:

$A=\frac{12\times 6}{2}=\frac{72}{2}=36$

7

Vt_custom_xy_xytriangle2

The above triangle has a base of and a height of . Find the length longest side (the hypotenuse).

$\sqrt{180}$

$\sqrt{144}$

Explanation

In order to find the length of the longest side of the triangle (hypotenuse), apply the formula:

, where and are equal to and , respectively. And, the hypotenuse.

Thus, the solution is:

$c=\sqrt{180}$

8

Vt_custom_xy_xytriangle_4

The above triangle has a height of and a base with length . Find the hypotenuse (the longest side).

Explanation

In order to find the length of the longest side of the triangle (hypotenuse), apply the formula:

, where and are equal to and , respectively. And, the hypotenuse.

Thus, the solution is:

$c=\sqrt{25}=5$

9

Vt_custom_xy_xytriangle_4

The above triangle has a height of and a base with length . Find the hypotenuse (the longest side).

Explanation

In order to find the length of the longest side of the triangle (hypotenuse), apply the formula:

, where and are equal to and , respectively. And, the hypotenuse.

Thus, the solution is:

$c=\sqrt{25}=5$

10

Vt_custom_xy_xytriangle_5

The triangle shown above has a base of length and a height of . Find the area of the triangle.

square units

square units

square units

square units

square units

Explanation

To find the area of this triangle apply the formula: $A=\frac{base\times height}{2}$

Thus, the solution is:

$A=\frac{7\times 5}{2}=\frac{35}{2}=17.5$

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