Question

What is the area of the figure below a. 7.5 b. 15 c. 21.25 d. 42.5

Answer 1

Check the picture below.

let's recall that in a Kite, the diagonals meet at 90° angles, therefore, we know the height of each of those 4 triangles, is 2.5 and 6, now, since the pair of triangles above are 45-45-90 triangles, we can use the 45-45-90 rule, as you see there, so, if the height is 2.5, then the base is also 2.5.

so, we really have 2 pair of triangles whose base is 2.5 and height of 2.5, and another pair of triangles whose base is 2.5 and height is 6, let's add their areas.

`\bf \stackrel{\textit{area of 2 triangles above}}{2\left[\cfrac{1}{2}(2.5)(2.5) \right]}~~+~~\stackrel{\textit{area of 2 triangles below}}{2\left[ \cfrac{1}{2}(2.5)(6) \right]}\implies 6.25+15\implies 21.25`

Answer 2

The correct answer is option C. 21.25

Explanation:

Formula:-

Area of triangle = bh/2

Where b - Base of triangle and h - Height of triangle

From the figure we can see a two isosceles triangle.

One triangle with base 5 m(2.5 + 2.5) and height 2.5 m

The second triangle with base 5 m and height 6

To find the area of first triangle

Here b = 5 m and h = 2.5 m

Area = bh/2 =(5 * 2.5)/2 = 6.25 m²

To find the area of second triangle

Here b = 5 m and h = 6 m

Area = bh/2 =(5 * 6)/2 = 15 m²

To find total area

Total area = Area of 1st triangle + area of 2nd triangle

= 6.25 + 15 = 21.25 m²

The correct answer is option C. 21.25