Question

The diagram shows rectangle abcd. aeb and dfc are straight lines. all measurements are in cm. the area of trapezium aedf is acm² express the area a in

Answer 1

The area of trapezium AEDF in its simplest form and in terms of x is
`10x^(2)+10x`
`cm^2`.

In Mathematics and Euclidean Geometry, a rectangle refers to a type of quadrilateral in which its opposite sides are equal and all the angles that are formed are right angles.

Based on the definition of a rectangle, we have the following congruent sides in rectangle ABCD;

AD = BC = 5x

AB = DC

AE + 2x = 6x + 2

AE = 6x - 2x + 2

AE = 4x + 2

The area of trapezoid AEDF can be calculated by using this mathematical equation (formula):

Area of trapezoid AEDF, A = 1/2 × (DF + AE) × AD

Area of trapezoid AEDF, A = 1/2 × (2 + 4x + 2) × 5x

Area of trapezoid AEDF, A = 1/2 × (4 + 4x) × 5x

Area of trapezoid AEDF, A = (2 + 2x) × 5x

Area of trapezoid AEDF, A =
`10x^(2)+10x`
`cm^2`

Complete Question:

The diagram shows rectangle ABCD. AEB and DFC are straight lines. All measurements are in cm. The area of trapezium AEDF is A
`cm^2` Express the area A in terms of x. Write your answer in its simplest form.

Answer 2

The area
`\( A \)` of trapezium
`\( AEDF \)` is
`\( A = (1)/(2)ac \)` square centimeters.

Step-by-step explanation

In the given rectangle
`\( ABCD \), \( AEB \)` and
`\( DFC \)` are straight lines, forming a trapezium
`\( AEDF \)`. The area of a trapezium is given by the formula
`\( A = (1)/(2)h(a + c) \)`, where
`\( h \)` is the height, and
`\( a \)` and
`\( c \)` are the lengths of the two parallel sides. In this case,
`\( AE \)` and
`\( DF \)` represent the bases of the trapezium, and
`\( AC \)` is the height.

To find the area
`\( A \)`, we substitute the given values into the formula. Let
`\( A \)` represent the area,
`\( AC \)` be the height,
`\( AE \)` be the shorter base, and
`\( DF \)` be the longer base. Therefore,
`\( A = (1)/(2) * AC * (AE + DF) \).`

Upon simplifying this expression, we obtain
`\( A = (1)/(2)ac \)`. This provides a straightforward way to calculate the area of trapezium
`\( AEDF \)` based on the lengths of its bases and the height
`\( AC \)` in the given rectangle
`\( ABCD \).`