How to find the area of a triangle - SSAT Middle Level Quantitative
Card 1 of 84
What is the area of a triangle with a base of 
and a height of 
?
What is the area of a triangle with a base of
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The formula for the area of a triangle is Area=\frac{1}{2}$times basetimes height.
Plug the given values into the formula to solve:
Area=\frac{1}{2}$times 12times 3
Area=\frac{1}{2}$times 36
Area=18
The formula for the area of a triangle is Area=\frac{1}{2}$times basetimes height.
Plug the given values into the formula to solve:
Area=\frac{1}{2}$times 12times 3
Area=\frac{1}{2}$times 36
Area=18
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A right triangle has legs 90 centimeters and 16 centimeters, What is its area?
A right triangle has legs 90 centimeters and 16 centimeters, What is its area?
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The legs of a right triangle are its base and height, so use the area formula for a triangle with these dimension. Setting 
:
The legs of a right triangle are its base and height, so use the area formula for a triangle with these dimension. Setting
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A triangle has base 18 inches and height 14 inches. What is its area?
A triangle has base 18 inches and height 14 inches. What is its area?
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Use the area formula for a triangle, setting 
:
Use the area formula for a triangle, setting
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What is the area of the above triangle?
What is the area of the above triangle?
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The two legs of a right triangle can serve as its base and its height. The area of the triangle is half the product of the two:
That is, the area is 84 square inches.
The two legs of a right triangle can serve as its base and its height. The area of the triangle is half the product of the two:
That is, the area is 84 square inches.
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What is the area of the above triangle?
What is the area of the above triangle?
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The two legs of a right triangle can serve as its base and its height. The area of the triangle is half the product of the two:
That is, the area is 3,000 square millimeters.
The two legs of a right triangle can serve as its base and its height. The area of the triangle is half the product of the two:
That is, the area is 3,000 square millimeters.
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Note: Figure NOT drawn to scale.
The above triangle has an area of 450 square centimers. 
. What is 
?
Note: Figure NOT drawn to scale.
The above triangle has an area of 450 square centimers.
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The area of a triangle is one half the product of its base and its height - in the above diagram, that means
.
Substitute 
, and solve for 
:
The area of a triangle is one half the product of its base and its height - in the above diagram, that means
Substitute
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Please use the following shape for the question. 
What is the area of this shape?
Please use the following shape for the question.
What is the area of this shape?
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From this shape we are able to see that we have a square and a triangle, so lets split it into the two shapes to solve the problem. We know we have a square based on the 90 degree angles placed in the four corners of our quadrilateral.
Since we know the first part of our shape is a square, to find the area of the square we just need to take the length and multiply it by the width. Squares have equilateral sides so we just take 5 times 5, which gives us 25 inches squared.
We now know the area of the square portion of our shape. Next we need to find the area of our right triangle. Since we know that the shape below the triangle is square, we are able to know the base of the triangle as being 5 inches, because that base is a part of the square's side.
To find the area of the triangle we must take the base, which in this case is 5 inches, and multipy it by the height, then divide by 2. The height is 3 inches, so 5 times 3 is 15. Then, 15 divided by 2 is 7.5.
We now know both the area of the square and the triangle portions of our shape. The square is 25 inches squared and the triangle is 7.5 inches squared. All that is remaining is to added the areas to find the total area. Doing this gives us 32.5 inches squared.
From this shape we are able to see that we have a square and a triangle, so lets split it into the two shapes to solve the problem. We know we have a square based on the 90 degree angles placed in the four corners of our quadrilateral.
Since we know the first part of our shape is a square, to find the area of the square we just need to take the length and multiply it by the width. Squares have equilateral sides so we just take 5 times 5, which gives us 25 inches squared.
We now know the area of the square portion of our shape. Next we need to find the area of our right triangle. Since we know that the shape below the triangle is square, we are able to know the base of the triangle as being 5 inches, because that base is a part of the square's side.
To find the area of the triangle we must take the base, which in this case is 5 inches, and multipy it by the height, then divide by 2. The height is 3 inches, so 5 times 3 is 15. Then, 15 divided by 2 is 7.5.
We now know both the area of the square and the triangle portions of our shape. The square is 25 inches squared and the triangle is 7.5 inches squared. All that is remaining is to added the areas to find the total area. Doing this gives us 32.5 inches squared.
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Find the area of the triangle.
Note: Figure not drawn to scale.
Find the area of the triangle.
Note: Figure not drawn to scale.
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To find the area of a triangle, multiply the base of the triangle by the height and then divide by two.
To find the area of a triangle, multiply the base of the triangle by the height and then divide by two.
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The hypotenuse of a right triangle is 25 inches; it has one leg 15 inches long. Give its area in square feet.
The hypotenuse of a right triangle is 25 inches; it has one leg 15 inches long. Give its area in square feet.
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The area of a right triangle is half the product of the lengths of its legs, so we need to use the Pythagorean Theorem to find the length of the other leg. Set 
:
The legs are 15 and 20 inches long. Divide both dimensions by 12 to convert from inches to feet:
feet
feet
Now find half their product:
square feet
The area of a right triangle is half the product of the lengths of its legs, so we need to use the Pythagorean Theorem to find the length of the other leg. Set
The legs are 15 and 20 inches long. Divide both dimensions by 12 to convert from inches to feet:
Now find half their product:
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The hypotenuse of a right triangle is 
feet; it has one leg 
feet long. Give its area in square inches.
The hypotenuse of a right triangle is
Tap to reveal answer
The area of a right triangle is half the product of the lengths of its legs, so we need to use the Pythagorean Theorem to find the length of the other leg. Set 
:
The legs have length 
and 
feet; multiply both dimensions by 
to convert to inches:
inches
inches.
Now find half the product:
The area of a right triangle is half the product of the lengths of its legs, so we need to use the Pythagorean Theorem to find the length of the other leg. Set
The legs have length
Now find half the product:
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What is the area of the triangle?
What is the area of the triangle?
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Area of a triangle can be determined using the equation:
Area of a triangle can be determined using the equation:
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A triangle has a height of 9 inches and a base that is one third as long as the height. What is the area of the triangle, in square inches?
A triangle has a height of 9 inches and a base that is one third as long as the height. What is the area of the triangle, in square inches?
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The area of a triangle is found by multiplying the base times the height, divided by 2.
Given that the height is 9 inches, and the base is one third of the height, the base will be 3 inches.
We now have both the base (3) and height (9) of the triangle. We can use the equation to solve for the area.
The fraction cannot be simplified.
The area of a triangle is found by multiplying the base times the height, divided by 2.
Given that the height is 9 inches, and the base is one third of the height, the base will be 3 inches.
We now have both the base (3) and height (9) of the triangle. We can use the equation to solve for the area.
The fraction cannot be simplified.
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What is the area (in square feet) of a triangle with a base of 
feet and a height of 
feet?
What is the area (in square feet) of a triangle with a base of
Tap to reveal answer
The area of a triangle is found by multiplying the base times the height, divided by 
.
The area of a triangle is found by multiplying the base times the height, divided by
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Note: Figure NOT drawn to scale.
What percent of the above figure is green?
Note: Figure NOT drawn to scale.
What percent of the above figure is green?
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The area of the entire rectangle is the product of its length and width, or
.
The area of the right triangle is half the product of its legs, or
The area of the green region is therefore the difference of the two, or
.
The green region is therefore
of the rectangle.
The area of the entire rectangle is the product of its length and width, or
The area of the right triangle is half the product of its legs, or
The area of the green region is therefore the difference of the two, or
The green region is therefore
of the rectangle.
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Note: Figure NOT drawn to scale.
Refer to the above diagram. Give the ratio of the area of the green region to that of the white region.
Note: Figure NOT drawn to scale.
Refer to the above diagram. Give the ratio of the area of the green region to that of the white region.
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The area of the entire rectangle is the product of its length and width, or
.
The area of the right triangle is half the product of its legs, or
The area of the green region is therefore the difference of the two, or
.
The ratio of the area of the green region to that of the white region is
That is, 11 to 4.
The area of the entire rectangle is the product of its length and width, or
The area of the right triangle is half the product of its legs, or
The area of the green region is therefore the difference of the two, or
The ratio of the area of the green region to that of the white region is
That is, 11 to 4.
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The quadrilateral in the above diagram is a square. What percent of it is white?
The quadrilateral in the above diagram is a square. What percent of it is white?
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The area of the entire square is the square of the length of a side, or
.
The area of the white right triangle is half the product of its legs, or
.
Therefore, the area of that triangle is
of that of the entire square.
The area of the entire square is the square of the length of a side, or
The area of the white right triangle is half the product of its legs, or
Therefore, the area of that triangle is
of that of the entire square.
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Mr. Jones owns the isosceles-triangle-shaped parcel of land seen in the above diagram. He sells the parcel represented in red to his brother. What is the area of the land he retains?
Mr. Jones owns the isosceles-triangle-shaped parcel of land seen in the above diagram. He sells the parcel represented in red to his brother. What is the area of the land he retains?
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The area of a triangle is half the product of its base and its height, so Mr. Jones's parcel originally had area
square meters.
The portion he sold his brother, represented by the red right triangle, has area
square meters.
Therefore, the area of the parcel Mr. Jones retained is
square meters.
The area of a triangle is half the product of its base and its height, so Mr. Jones's parcel originally had area
The portion he sold his brother, represented by the red right triangle, has area
Therefore, the area of the parcel Mr. Jones retained is
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Find the area of the triangle below
Find the area of the triangle below
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The equation for area of a triangle is
.
In this case the coordinates of the base are 
, which means the length of the base is 
.
The coordinates of the side that determines the height are 
.
Therefore the height is 
.
.
The equation for area of a triangle is
In this case the coordinates of the base are
The coordinates of the side that determines the height are
Therefore the height is
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The above diagram shows Rectangle 
, with midpoint 
of 
.
The area of 
is 225. Evaluate 
The above diagram shows Rectangle
The area of
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is the midpoint of 
, so 
has as its base 
; its height is 
.
Its area is half their product, or
Set this equal to 225:
.
Its area is half their product, or
Set this equal to 225:
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Give the perimeter of the above triangle in feet.
Give the perimeter of the above triangle in feet.
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The perimeter of the triangle - the sum of the lengths of its sides - is
inches.
Divide by 12 to convert to feet:
As a fraction, this is 
or 
feet,
The perimeter of the triangle - the sum of the lengths of its sides - is
Divide by 12 to convert to feet:
As a fraction, this is
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