# Given below is the area of three triangles. Fill in the blanks with their base or height as applicable.

Last updated date: 25th Mar 2023

•

Total views: 309.3k

•

Views today: 5.86k

Answer

Verified

309.3k+ views

Hint: Here, we will proceed by using the formula of the area of the triangle.

We know that the area of triangle = $\frac{1}{2} \times base \times height$

From the given data, we have

In first row, measurements of base and area of a triangle are given as

$base = 15cm$ and $area = 87c{m^2}$

Substituting these values in the formula of area of triangle, then

$\therefore 87 = \frac{1}{2} \times 15 \times height$

$ \Rightarrow height = \frac{{87 \times 2}}{{15}} = 11.6cm$

In second row, measurement of height and area of a triangle are given as

$height = 31.4cm$ and $area = 1256m{m^2}$

Substituting these values in the formula of area of triangle, then

$\therefore 1256 = \frac{1}{2} \times base \times 31.4$

$ \Rightarrow base = \frac{{1256 \times 2}}{{31.4}} = 80cm$

In third row, measurements of base and area of a triangle are given as

$base = 22cm$ and $area = 170.5c{m^2}$

Substituting these values in the formula of area of triangle, then

$\therefore 170.5 = \frac{1}{2} \times 22 \times height$

$ \Rightarrow height = \frac{{170.5 \times 2}}{{22}} = 15.5cm$

We got all the missing values of the given data.

Thus, the missing values in the given table are:

Note: To find the area enclosed by a triangle, we multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles. That means, the area of each triangle is equal to one-half the area of the parallelogram. While calculating the area, we need to make sure that the base and height are in the same units (like cm or mm). If they are not in the same units, we need to convert them into the same units.

We know that the area of triangle = $\frac{1}{2} \times base \times height$

From the given data, we have

In first row, measurements of base and area of a triangle are given as

$base = 15cm$ and $area = 87c{m^2}$

Substituting these values in the formula of area of triangle, then

$\therefore 87 = \frac{1}{2} \times 15 \times height$

$ \Rightarrow height = \frac{{87 \times 2}}{{15}} = 11.6cm$

In second row, measurement of height and area of a triangle are given as

$height = 31.4cm$ and $area = 1256m{m^2}$

Substituting these values in the formula of area of triangle, then

$\therefore 1256 = \frac{1}{2} \times base \times 31.4$

$ \Rightarrow base = \frac{{1256 \times 2}}{{31.4}} = 80cm$

In third row, measurements of base and area of a triangle are given as

$base = 22cm$ and $area = 170.5c{m^2}$

Substituting these values in the formula of area of triangle, then

$\therefore 170.5 = \frac{1}{2} \times 22 \times height$

$ \Rightarrow height = \frac{{170.5 \times 2}}{{22}} = 15.5cm$

We got all the missing values of the given data.

Thus, the missing values in the given table are:

Base | Height | Area of triangle |

15cm | 11.6cm | 87$c{m^2}$ |

80mm | 31.4mm | 1256$m{m^2}$ |

22cm | 15.5cm | 170.5$c{m^2}$ |

Note: To find the area enclosed by a triangle, we multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles. That means, the area of each triangle is equal to one-half the area of the parallelogram. While calculating the area, we need to make sure that the base and height are in the same units (like cm or mm). If they are not in the same units, we need to convert them into the same units.

Recently Updated Pages

If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main

If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main

If abcdare any four consecutive coefficients of any class 11 maths JEE_Main

If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main

If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main

One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?