Question

In trapezoid, two triangles are formed by the bases and the intersecting diagonal segments. The areas of these triangles are S1 and S2. Find area of the trapezoid in terms of S1 and S2.

Answer 1

Since we know that we can find area of a trapezoid by dividing our trapezoid into two triangles with parallel sides of trapezoid as bases of our triangles. The area of trapezoid is sum of the areas of these two triangles.

We have been given that areas of our triangles are $S_1$ and $S_2$. We can find area of our trapezoid by adding areas of our both triangles.    

$\text{Area of trapezoid}=S_1+S_2$

Therefore, area of our trapezoid will be $S_1+S_2$.  

   

Answer 2

Area of trapezoid in terms of ${S_1}$ and ${S_2}$ is $\boxed{{\text{Area of trapezoid}} = {S_1} + {S_2}}.$

Further explanation:

The formula of area of trapezoid can be expressed as follows,

$\boxed{{\text{Area of trapezoid}} = \frac{1}{2} \times \left( {{\text{sum of parallel sides}}} \right) \times {\text{height}}}$

Given:

Two triangles are formed by the bases and the intersecting diagonal segments. The areas of these triangles are ${S_1}$ and ${S_2}.$

Explanation:

Consider a trapezoid ABCD, the diagonal of the trapezoid is AC. Cut the trapezoid into two halves to obtain the two triangles.

The area of triangle ABC is ${S_1}$ and the area of triangle ADC is ${S_2}.$

The area of trapezoid can be obtained as follows,

$\begin{aligned}{\text{Area of trapezoid}}&= {\text{Area of triangle ABC}} + {\text{Area of triangle ADC}}\\&= {S_1} + {S_2}\\\end{aligned}$

The area of trapezoid in terms of ${S_1}$ and ${S_2}$ is $\boxed{{\text{Area of trapezoid}} = {S_1} + {S_2}}.$

Kindly refer to the image attached.

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Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Triangles

Keywords: triangle, triangle pair, equal angles, sides, area, trapezoid, two triangles, bases, intersecting, diagonal, segment, sector, minor segment.