Questions & Answers

Question

Answers

Answer

Verified

158.1k+ 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.