Question

Find the area of each of the following figure:

Answer 1

Clearly opposite sides of quadrilateral PQRT are parallel, it is a parallelogram.
ST
= SR - TR
= 30 - 22
= 8cm
In ΔPST,
Let a = PS = 10cm, b = ST = 8cm and C = TP = 10cm

∴ s = `("a" + "b" + "c")/(2)`

= `(10 + 8 + 10)/(2)`

= `(28)/(2)`
= 14cm
Area of ΔPSR
= `sqrt("s"("s"- "a")("s" - "b")("s"-"c")`
= `sqrt(14(14 - 10)(14 - 8)(14 - 10)`
= `sqrt(14 xx 4 xx 6 xx 4)`
= `8sqrt(21)"cm"^2`
If PM is taken height corresponding to base ST,
Area of ΔPST

= `(1)/(2) xx "ST" xx "PM"`

⇒ `8sqrt(21) = (1)/(2) xx 8 xx "PM"`

⇒ PM = `2sqrt(21)"cm"`
∴ Area of given figure

= `(1)/(2) xx("PQ" + "SR") xx "PM"`

= `(1)/(2) xx (22 + 30) xx 2sqrt(21)`

= `(1)/(2) xx 52 xx 2sqrt(21)`
= `52sqrt(21)"cm"^2`.