Question

A Parallelogram PRTV is made up of triangle PQV and trapezoid QRTU. The area of the parallelogram PRTV is 96 square feet. The length of TU and UV are equal. And Between RT there is a right angle RS to St which the height to the right angle is 8 ft. Find the area of the triangle QUV

Answer 1

The area of triangle QUV = 24 ft^2

Explanation:

Area of a parallelogram = base × height

A = b×h ....1

Given;

Area of parallelogram PRTV = 96 ft^2

Height of parallelogram PRTV = 8 ft

From equation 1

base length of parallelogram PRTV = A/h = 96/8 = 12 ft

From the question, TU = UV

TV = TU + UV = 2UV

UV = TV/2

For more clarity, see attached image

And length TV = base length of parallelogram PRTV

TV = 12 ft

So,

UV = TV/2 =12/2 = 6 ft

Area of triangle = 1/2 × base × height

For triangle QUV

base = UV = 6ft

height = 8ft

Area of triangle QUV = 1/2 × 6ft × 8ft = 24 ft^2

The area of triangle QUV = 24 ft^2