What is the area of the trapezoid with height 10 units? Enter your answer in the box. units2 A rectangle with a length of 5 and a height of 10 has two triangles on each side of it with long leg lengths of 12.

If by "long leg lengths" you mean the hypotenuse then the area is 116 sq. units. If you mean the bases of the triangles then the area is 170 sq. units.

If the length of 12 is the hypotenuse, we first must find the base of the triangles using the Pythagorean theorem:

10² + b² = 12²
100 + b² = 144
b² = 44
b = √44 = 6.6

This means we have two triangles and a rectangle. The area of the rectangle is 5(10) = 50 sq. units. The area of each triangle is 1/2(6.6)(10) = 33. Adding all 3 together we have:

50+33+33 = 116 sq. units.

If the 12 is the base, then we have the rectangle with the area of 5(10) = 50 and two triangles each with an area of 1/2(12)(10) = 60:

50+60+60 = 170 sq. units.

Yogeshkumari Yogeshkumari · Answer 2 · 2022-07-20T06:16:23+02:00

The area of a given trapezoid is equal to [tex]85[/tex] square units.

What is the area?

" Area is defined as the total space occupied by two-dimensional object enclosed in it."

Formula used

Area of a rectangle [tex]= l \times h[/tex]

[tex]l=[/tex] length of a rectangle

[tex]h=[/tex] height of a rectangle

Area of a triangle [tex]= \frac{1}{2} \times base \times height[/tex]

According to the question,

Given,

Height of a trapezoid and rectangle [tex]= 10[/tex] units

Length of a rectangle [tex]= 5[/tex] units

As shown in the drawn figure,

Length of long leg of trapezoid [tex]= 12[/tex] units

Trapezoid divided into three parts two triangles and a rectangle.

Base length of a rectangle [tex]= 5[/tex] units

Consider both the triangle with equal base we get,

Base length of a each triangle [tex]= \frac{1}{2} (12- 5)[/tex]

[tex]= 3.5[/tex] units

Substitute the value in the formula we have,

Area of a rectangle [tex]= 5 \times 10[/tex]

[tex]=50[/tex] square units ________[tex](1)[/tex]

Area of each triangle [tex]= \frac{1}{2} \times 3.5 \times 10[/tex]

[tex]= 17.5[/tex] square units ________[tex](2)[/tex]

From the drawn figure we have,

Area of a trapezoid ABEF

= Area of triangle AED + Area of rectangle ABCD + Area of triangle BCF

Substitute the value from [tex](1)[/tex] and [tex](2)[/tex] we get,

Area of a trapezoid ABEF [tex]= 17.5 + 50 + 17.5[/tex]

[tex]= 85[/tex] square units

Hence, the area of a given trapezoid is equal to [tex]85[/tex] square units.

Learn more about area here

brainly.com/question/27683633

#SPJ2