examples with solutions for area of a right triangle
Exercise #1
What is the area of the triangle in the drawing?
Video Solution
Step-by-Step Solution
First, we will identify the data points we need to be able to find the area of the triangle.
the formula for the area of the triangle: height*opposite side / 2
Since it is a right triangle, we know that the straight sides are actually also the heights between each other, that is, the side that measures 5 and the side that measures 7.
We multiply the legs and divide by 2
25×7=235=17.5
Answer
17.5
Exercise #2
The triangle ABC is given below. AC = 10 cm
AD = 3 cm
BC = 11.6 cm What is the area of the triangle?
Video Solution
Step-by-Step Solution
The triangle we are looking at is the large triangle - ABC
The triangle is formed by three sides AB, BC, and CA.
Now let's remember what we need for the calculation of a triangular area:
(side x the height that descends from the side)/2
Therefore, the first thing we must find is a suitable height and side.
We are given the side AC, but there is no descending height, so it is not useful to us.
The side AB is not given,
And so we are left with the side BC, which is given.
From the side BC descends the height AD (the two form a 90-degree angle).
It can be argued that BC is also a height, but if we delve deeper it seems that CD can be a height in the triangle ADC,
and BD is a height in the triangle ADB (both are the sides of a right triangle, therefore they are the height and the side).
As we do not know if the triangle is isosceles or not, it is also not possible to know if CD=DB, or what their ratio is, and this theory fails.
Let's remember again the formula for triangular area and replace the data we have in the formula:
(side* the height that descends from the side)/2
Now we replace the existing data in this formula:
2CB×AD
211.6×3
234.8=17.4
Answer
17.4
Exercise #3
Calculate X using the data in the figure below.
Video Solution
Step-by-Step Solution
The formula to calculate the area of a triangle is:
(side * height descending from the side) /2
We place the data we have into the formula to find X:
20=2AB×AC
20=2x×5
Multiply by 2 to get rid of the fraction:
5x=40
Divide both sections by 5:
55x=540
x=8
Answer
8
Exercise #4
Which of the following triangles have the same areas?
Video Solution
Step-by-Step Solution
We calculate the area of triangle ABC:
212×5=260=30
We calculate the area of triangle EFG:
26×10=260=30
We calculate the area of triangle JIK:
26×5=230=15
Therefore, the triangles that have the same areas are ABC and EFG.
Answer
EFG and ABC
Exercise #5
The area of triangle ABC is 20 cm².
Its height (AD) is 8.
Calculate the length of the side BC.
Video Solution
Step-by-Step Solution
We can present the data in the formula to calculate the area of the triangle:
S=2AD×BC
20=28×BC
Cross multiplication:
40=8BC
Divide both sides by 8:
840=88BC
BC=5
Answer
5 cm
Question 1
PRS is a triangle.
The length of side SR is 4 cm. The area of triangle PSR is 30 cm².